KYIV, Ukraine — Despite suffering grievous losses over nearly six months of war, Russia still holds a distinct advantage over Ukraine in a head-to-head fight featuring brutal artillery battles. But Ukraine’s military has achieved some new battlefield success, waging the war on its own terms.

Supplied with a growing arsenal of long-range Western weapons and aided by local fighters known as partisans, Ukraine has been able to hit Russian forces deep behind enemy lines, disrupting critical supply lines and, increasingly, striking targets that are key to Moscow’s combat potential.

One blow to the Russians this week was a series of explosions at an air base on the occupied Crimean Peninsula that destroyed at least eight warplanes, and that a Ukrainian official said had resulted from a strike carried out by special forces troops aided by local partisan fighters.

The new approach has been particularly well suited to the Kherson region in the south, where for weeks Ukrainian officials have been engaged in the opening salvos of a counteroffensive. The city of Kherson in particular, dependent for supplies on just four bridges spanning the Dnipro River, is considered more vulnerable than other occupied cities.

On Saturday, the Ukrainians claimed to have hit the last of those four key bridges, leaving thousands of Russian troops in danger of becoming isolated and cut off from resupply, according to Western intelligence officials.

“We do not have the resources to litter the territory with bodies and shells, as Russia does,” Ukraine’s defense minister, Oleksii Reznikov, said in an interview this past week with Pravda, a Ukrainian news media outlet. “Therefore it is necessary to change tactics, to fight in a different way.”

The strategy seems to be producing some results. While the Ukrainian military has not made major territorial gains, it has managed to slow the Russian advance across the country, for now, at least, and stanch the heavy losses Ukraine was suffering in recent months, which had led to wavering morale and some soldiers even deserting their platoons.

But the Russians have continued to apply pressure in the east and the south on Ukrainian frontline positions, with some that are slowly buckling. The incremental advances have indicated that despite setbacks from Ukraine’s attacks, the Russian military effort still has enough forces to continue offensive operations.

Ukraine’s efforts in the south represent less a change in approach than an extension, with the aid of new longer-range weapons, of a strategy adopted at the start of the war meant to level the playing field with Russia. With the Russian army far outmatching Ukraine’s forces in the number of troops, weapons and ammunition, Ukraine’s military has had to be innovative and nimble.

“It’s clear the Ukrainians can’t match the Russians unit for unit and soldier for soldier. And Ukraine, like the Russians, is running out of soldiers,” said Samuel Bendett, a Russian weapons analyst at the Center for Naval Analysis. “So Ukraine has to be very judicial in how they draw out the Russian forces.”

Ukraine successfully repelled Russia’s efforts to seize the capital, Kyiv, using smaller, adaptable fighting units that exploited its home-field advantage for lightning attacks on Russian forces, which were concentrated in large lumbering columns that made easy targets.

In the east, with its wide, flat plains, Russia initially was able to take advantage of its superiority in numbers and firepower, wearing down the Ukrainian troops with relentless artillery barrages before moving to seize territory.

But now, supplied with new longer-range artillery pieces, like the American-made High Mobility Artillery Rocket System or HIMARS, Ukraine has been able to slow Russia’s advance and divert some attention to what Ukraine’s generals see as more advantageous territory in the south.

It is there, particularly in the Kherson region, which was the first region of Ukraine lost to Russian forces, that Ukraine hopes it can begin to turn the tide of the war. Using HIMARS and other long-range weapons, Ukrainian forces have slowly chipped away at Russia’s ability to supply troops holding territory west of the Dnipro River, including the city of Kherson, which Russian forces have controlled since the first weeks of the war.

Serhii Khlan, an adviser to the head of the Kherson region’s military administration, said on Facebook that the destruction of the final remaining bridge over the Dnipro River on Saturday was part of Ukraine’s strategy to frustrate the Russian forces.

“Of course, they will try to repair, look for an alternative in the crossings,” he said. “But it is time, money, and then as soon as they prepare and gain equipment and strength — we will destroy it again.”

The idea, according to Ukrainian commanders, is to make conditions so untenable that Russia withdraws across the Dnipro on its own in the face of the expected Ukrainian counterattack.

“Our soldiers are inventive and progressive, while the Russians are working by the book, deploying battle formations as it was laid out in the Soviet Union,” Vitaliy Kim, the head of the Mykolaiv region’s military administration, said in an interview last week. “Our guys have read this book and understand it perfectly well, and are using it for their own goals.”

In eastern Ukraine, the main Russian effort is now focused on trying to gain ground in the Donetsk region, and there has been intense fighting in recent days in the area around the town of Pisky. Russia’s Defense Ministry said on Saturday that the town had fallen, a claim that could not be independently verified.

The Ukrainian way, as is becoming more apparent by the day, is to carry out strikes that undermine Moscow’s ability to sustain the forces it has deployed at the front.

“We look for the weak points of the Russians, determine the critical points of the enemy and gradually bleed them,” Andrii Ryzhenk, a former top Ukrainian military official who is now an adviser at the Center for Defense Strategies, a Ukrainian think tank, said this month.

While the approach has been aided by the long-range Western weapons, it has also been encouraged by Western officials. Mr. Reznikov, Ukraine’s defense minister, said this week that the American and British defense ministers had both offered him a piece of advice: “The Russians use meat-grinder tactics — if you plan to fight them with the same tactics, we will not be able to help you.”

Critical to Russia’s efforts to hold onto land in Ukraine’s south is Moscow’s control over Crimea, which Russia illegally annexed in 2014. Before its full-scale invasion of Ukraine early this year, Moscow sent tens of thousands of soldiers to the peninsula, and they captured large swaths of the southern regions of Kherson and Zaporizhzhia within days.

Since then, rail lines from Crimea have been critical in enabling Moscow to move heavy weapons and equipment into southern Ukraine. Last week, Britain’s Defense Intelligence Agency said that the Ukrainians had hit a key railroad line from the peninsula, making it “highly unlikely the rail link connecting Kherson with Crimea remains operational.”

The Russians are likely to race to repair it, the agency said, but the attack underscored a critical vulnerability.

The southern theater is now essentially cut in two — divided by the Dnipro River — and the British intelligence agency said that even if Russia managed to make significant repairs to the bridges that Ukrainian forces have hit, the structures would remain a potential weak spot.

Marc Santora reported from Kyiv, Ukraine, Michael Schwirtz from Odesa, Ukraine, and Jack Nicas from Rio de Janeiro. Thomas Gibbons-Neff contributed reporting.