In the PTO - it may be this ;
August 15, 1945.
3 Seafires of Fleet Air Arm 887 Sqn and 4 Seafires of 894 Sqn from the carrier Indefatigable engaged 12 Zeros of 302nd Kokutai (Naval Air Group) over Tokyo Bay, while escorting 6 Avengers of 820 Sqn and 4 Fireflies of 1772 Sqn.
FAA losses after the engagement were one Avenger and one Seafire (Sub Lt Hockley as mentioned in a previous post).
The Allied claims were 4 Zeros.
Although a confused action, it is very possible that Sub Lt Gerry Murphy, who destroyed 2 Zeros (confirmed) had actually fired the last shots of the final dogfight of WW2.
However, there were incidents between the Japanese and Russians which may have been later and maybe hard to confirm?