[GuerraCivil]

True - air-to-air rockets were used in WW1 against observation balloons. So lets be more precise: the Soviet RS-82 rockets were the first air-to-air rockets (or unguided missiles) to be used against enemy aircraft. Wiki based on Soviet aviation historian Mikhail Maslov:

"...the earliest known use by the Soviet Air Force of aircraft-launched unguided anti-aircraft rockets in combat against heavier-than-air aircraft took place in August 1939, during the Battle of Khalkhin Gol. A group of Polikarpov I-16 fighters under command of Captain N. Zvonarev were using RS-82 rockets against Japanese aircraft, shooting down 16 fighters and 3 bombers in total..."

Of the very first encounter of RS-82 I have read that two Japanese planes were reportedly shot down in air combat, but these losses are not confirmed by Japanese sources. IIRC, the Japanese mistakenly reported of this first encounter that they were attacked by flak instead of rockets. They did see some rather mysterious explosions but could not see the cause of them. Did Japanese actually at any point of Khalkin Gol conflict realize that the enemy was using air-to-air rockets?

Anyway Soviets considered the first combat tests of RS-82 as promising. But perhaps that was based on too optimistic combat reports of Soviet pilots, and RS-82 was a controversial weapon - rocket equipped fighters were slow and clumsy and the possibility for successful hits was low.

Of the other later encounters I do not know if any of the Soviet claims with RS-82 have been confirmed by Japanese combat reports. The Japanese at that time flew in disciplined and very tight formations, which were quite ideal targets for rocket attacks so I would not be surprised that some Japanese planes were destroyed or damaged by Soviet rocket attacks.