Able to pick off Russian military bases, ammunition depots and infrastructure far behind front lines, Ukraine’s 16 Himars helped its troops this summer halt a bloody Russian advance. Since last month, Ukrainians have seized back swaths of territory in their country’s east and ground down Russian troops in the south. Washington recently pledged to deliver another 18 Himars.

Within Kyiv’s arsenal, Himars offer a unique combination of range, precision and mobility that allows them to do the job traditionally handled by dozens of launchers firing thousands of shells.

By shrinking launchers and nearly guaranteeing hits on targets, Himars and the other equipment are upending century-old assumptions about how wars must be fought—and particularly about military supplies. Himars’s vastly improved accuracy also collapses the massive logistical trail that modern infantry has demanded.

“Himars is one part of a precision revolution that turns heavily equipped armies into something light and mobile,” said

Robert Scales,

a retired U.S. Army major general who was among the first to envision Himars in the 1970s.

Last month The Wall Street Journal gained rare access to a front-line Himars unit.

One evening at dusk the men in this unit were making dinner when orders for their fifth mission of the day arrived: to target Russian barracks and a river barge ferrying munitions and tanks 40 miles away.

Six men piled into their two Himars: a driver, targeter and commander in each, accompanied by the battery commander and a security detail in an armored personnel carrier. The commander plugged coordinate data into a tablet computer to determine the safest location for firing.

Within minutes, the two Himars rumbled out from cover under an apricot grove toward the launch spot in a nearby sunflower field. Thirty seconds after arriving, they fired seven missiles in quick succession. Before the projectiles hit their targets, the trucks were returning to base camp.

Ten minutes later came another pair of targets: Soviet-era rocket launchers some 44 miles away. Off rolled the Himars again and fired another barrage of missiles.

Soon after, the soldiers were back at camp and finishing their dinner. Some pulled up videos on Telegram showing the fruit of their labor: burning Russian barracks.

Ukraine’s Himars rockets, which can fly 50 miles, have hit hundreds of Russian targets, including command centers, ammunition depots, refueling stations and bridges, choking off supplies to front-line units. Since stopping Russia’s spring advance across Ukraine’s eastern Donbas region, they are now targeting retreating Russian forces.

Ukrainian commanders estimate that Himars are responsible for 70% of military advances on the Kherson front, the unit’s commander, Lt.

Valentyn Koval,

said. The four vehicles in his unit have killed hundreds of Russians and destroyed about 20 antiaircraft batteries, he said.

Russian artillery—like most such systems since World War I—lacks precision. To destroy a target, troops generally level everything around it. Gunners following maps rain shells in a grid pattern that aims to leave no terrain in a quadrant untouched. Russian forces in Ukraine are lobbing dozens of shells per acre to hit one objective, analysts say.

Himars can do the job with one rocket carrying a 200-pound explosive warhead. Each Ukrainian Himars carries one six-rocket pod that can effectively land the punch of more than 100,000 lbs. of traditional artillery.

Artillery is cumbersome. During Operation Desert Storm in Iraq in 1991, it accounted for more than 60% of a U.S. division’s weight. Moving it demands soldiers, trucks, fuel and time, plus additional soldiers and vehicles to protect those supply operations.

All that support sucks resources and makes a juicy target, as the world saw in the opening days of the Ukraine war, when a Russian supply convoy halted by Ukrainian attacks outside Kyiv became a 40-mile-long sitting duck.

“It’s not just the precision of Himars that’s revolutionary,” said Gen. Scales. “It’s the ability to reduce the tonnage requirements by an order of magnitude or better.”

The supply chain for Himars units consists of factory-packaged rocket pods stashed at pickup points in the nearby countryside and usually hidden by foliage. A cargo truck deposits the camouflage-green pods—each a little bigger than a single bed—at a string of designated locations, not unlike a commercial delivery route.

Himars teams drive to the ammo drop spots, where a waiting three-man loading team removes spent pods and swaps in full ones within five minutes, using a crane integrated into the vehicle.

“Himars is one of, if not the most, efficient type of weapons on the battlefield,” said Lt. Koval, a jocular 22-year-old with a Pokémon ringtone on his cellphone. “This gives us an opportunity to react quickly, hit in one place, move to another, and destroy effectively.”

Russia’s best truck-based rocket launchers, by contrast, can require around 20 minutes to set up in the launch spot and 40 minutes to reload—critical time when the enemy tries to return fire. The Himars can drive faster and has an armored crew cabin.

Ukrainian Himars teams stay lean by spending weeks in the field without returning to a larger base. Lt. Koval’s unit, which received the first Himars in June, has spent the past three months sleeping in tents beside the launchers or inside nearby support vehicles.

The men, trained by U.S. instructors outside Ukraine, remain on standby for new targets, switching into action and just as casually returning to mundane activities like making coffee or playing cards.

On the front armor of one Himars, the soldiers painted a white grin below the Ukrainian word for “workhorse.” On the other, whose odometer shows it has traveled over 13,000 miles, they stenciled 69 black skulls, commemorating significant confirmed hits.

Mission details arrive as geographic coordinates, with a target description and instructions on whether to use explosive missiles for armored targets or fragment charges for hitting personnel. Targeting tips come from sources including U.S. intelligence and partisans in occupied territories.

The Himars commanders then pick a suitable launch location and guide the vehicles into place. Inside the cab, the vehicle commander sits between the driver and the targeter, who feeds the mission data into a computer. When the vehicle reaches the launch site, the targeter presses one button to angle the missiles skyward and another button to fire.

The missiles roar into the night sky with a burst of flame, leaving a cloud of smoke over the field. The launcher is lowered and the vehicle speeds back to its tree cover.

“We are the juiciest target in the region,” said Lt. Koval. “So we need to maneuver to survive.”

Maneuverability is exactly why Himars was created as a downsized version of a tank-like weapon, the Multiple Launch Rocket System, which has also been provided to Ukraine by the U.K. and Germany. First used in Desert Storm, before the advent of precision artillery, massed batteries of the 12-rocket vehicles unleashed so much explosive force and shrapnel that Iraqi troops dubbed it “steel rain.”

MLRS’s heft means that only the largest military cargo jets can airlift it and they land far from the fighting. To move distances on land requires a flatbed truck. Himars was envisioned as a lighter, more agile version.

The push for nimble units equipped with lightweight gear became part of a broader effort to streamline the U.S. military after the Cold War that reached its peak under Defense Secretary

Donald Rumsfeld

starting in 2001, but was sidetracked by wars in Afghanistan and Iraq.

Himars, on wheels and with only six rockets, was a project that stayed on track. One initial shortcoming, the Pentagon discovered, was that six cluster bombs didn’t pack enough punch to destroy many targets. GPS-guided artillery, rolled out in the mid-1990s, gave Himars new life. Precision meant the rockets didn’t need to explode together for a giant blast. They could each pick off a different geolocated target.

“The precision revolution changes everything,” said Gen. Scales, who considers the transformation to be the kind of epoch-making military shift that redefines warfare and will now tip battlefield advantage from massed armies to small infantry units.

Such shifts were rare in the past, including the eclipse of infantry by horse-mounted warriors around the fourth century and the introduction of gunpowder to Europe a millennium later, said Gen. Scales, a military historian who served as commandant of the U.S. Army War College.

Others came around the U.S. Civil War with the introduction of precise rifles and artillery and machine guns, which proved so deadly in World War I, and at the start of World War II, when the German blitzkrieg merged motorized transportation with radio coordination of troops.

Now, inexpensive microprocessors are putting what Gen. Scales dubs “cheap precision” in the hands of Ukrainian soldiers.

“If I enter the coordinates of this hole,” said Lt. Koval, standing by a molehill the size of a shoebox, “it will hit this hole.”

On one particularly busy day in late August, the two Himars under Lt. Koval’s command worked in tandem with two others. When his pair ran out of ammunition, they dropped back to reload while the other duo advanced to fire. Lt. Koval said they tag-teamed for 37 hours without stopping to sleep and hit roughly 120 targets, enabling Ukrainian infantry to break Russian lines around the southern city of Kherson.

Washington was initially reluctant to provide Ukraine with Himars, fearing such a move could cause Moscow to retaliate against the U.S. or its allies in the North Atlantic Treaty Organization. It has declined to supply more powerful rockets which can be fired up to 185 miles and would enable Ukraine to destroy sturdier targets, like concrete bridges that they have so far only been able to blow holes through.

In a sign that Ukraine’s additional firepower is taking a toll on Moscow’s forces, Russian Defense Minister

Sergei Shoigu

has told Russian troops to make Ukraine’s long-range weaponry a priority target.

Himars operators say the biggest threat comes from Russia’s kamikaze drones, buttressed recently by more effective Iranian systems, but they feel well protected by Ukrainian anti-air systems and special forces. Lt. Koval’s crew abandoned two firing missions this summer out of caution when a drone was spotted nearby, but he said no Himars have been hit.

“We’re always on the move,” said Lt. Koval.

Write to Stephen Kalin at stephen.kalin@wsj.com and Daniel Michaels at daniel.michaels@wsj.com