Russell Westbrook added 21 points, 17 assists and 15 rebounds in the win, moving him past Jason Kidd for third place on the NBA's all-time triple-doubles list.
Westbrook reached his 108th triple-double when the Thunder trailed by 17. He is 30 behind Magic Johnson for second place and 73 behind all-time leader Oscar Robertson.
Allen Crabbe led the Nets with 22 points, but was scoreless in the final 12 minutes as Brooklyn's home losing streak and overall losing streak reached seven games.
The Thunder trailed 99-80 with 8:53 remaining. George would cut the lead to single digits at 105-97 at the 5:34 mark, and his layup with 1:43 left to cut the deficit to 112-111.
After Oklahoma City called its last timeout with 8.1 seconds left, Schroder inbounded to Westbrook, who was covered by Crabbe. Westbrook passed it to George, who took one dribble and then hit a 3-pointer from the right wing near Brooklyn's bench. It was from a similar spot as Philadelphia's Jimmy Butler game-winner on Nov. 26.
On the next possession, Westbrook deflected Jared Dudley's dribble out of bounds, leaving 0.1 seconds remaining. The game ended when Steven Adams deflected Harris' inbounds pass out of bounds.
Before the dramatic comeback, Westbrook was at 21 points, 15 rebounds and 12 assists as Oklahoma City faced a 93-75 deficit entering the fourth. The Nets held their 23-point lead with 4:17 left in the third on a basket by Dinwiddie.