The only time the Soviet Union officially fought the US was in brutal air combat
In October 1944, WWII was still raging all across Europe. On the Eastern Front, Red Army troops in Yugoslavia were making their way to bolster other Soviet forces in the region when American P-38 Lightning fighters started raining lead on them.
In response, the Soviet Air Force launched two groups of its premiere fighter of the time, the Yakovlev Yak-3. The Yaks fought the Yanks for a good 15 minutes over the Yugoslav (now Serbia) town of Niš. No one knows exactly how or where the error started, but each side fought the other viciously, thinking they were fighting Nazis.
The Americans' small taste of the brutality of Eastern Front combat cost dozens of Soviet and American lives.
The Soviets claimed the American fighters were 400 kilometers off course, and thus saw the Red Army ground forces as an unknown German force. Others believe the meetup was intentional, but that the Red Army moved faster than anticipated. When the Americans encountered a significant force 100 kilometers ahead of the expected Allied position, they engaged.
No matter what, the result was an intense air battle that both countries have kept classified for decades. Norwich University calls it the 8th largest air battle in history, even though the exact number of American fighters is unknown.
In fact, most official details are still classified, but both the United States and Russia admit the event occurred. An estimated 30 Soviet ground troops and airmen died in the fighting and Soviet accounts tell of P-38 fighters being shot down.
Another account of the battle, from Soviet Colonel Nikolai Shmelev, details American fighters strafing the airfields near Niš as Russian Yakovlev-9 planes were taxiing to fend off the U.S. Lightnings.
This would not be the only time Soviet and American fighter pilots would tangle with each other in the coming years. They would also fight (unofficially) over the Korean Peninsula and Vietnam, not to mention the numerous Cold War incidents of airspace violations and interceptions.
Enjoy some WWII gun camera footage from the P-38: