The Thunder trailed by seven with 2 1/2 minutes left before rallying to take the first step toward avenging a 4-1 series loss a year ago.
''It's the playoffs,'' Durant said. ''No matter how it gets done, you've got to do it.''
With his team trailing by one late in the fourth quarter, he forced his way toward the lane and found himself with defenders closing in and the clock winding down.
Durant maneuvered to the free throw line and got off a high-arcing shot over Shawn Marion that hit off the front of the rim and then off the backboard before falling through the net.
The defending NBA champion Mavericks, who were out of timeouts, could not get a shot off before the buzzer.
''If you have a timeout, you can move the ball (to half-court) and maybe have a look at it,'' said Dirk Nowitzki, who had hit two free throws with 9 seconds left to put Dallas ahead. ''But if you don't have a timeout, that's definitely a buzzer-beater.''
Nowitzki scored 11 of his 25 points in the final 5 minutes, going on a personal 7-1 run that made it 92-85 with 3:23 to go.
He then answered Russell Westbrook's layup with a foul line jumper to restore the seven-point advantage, but it didn't prove to be enough.
''It's tough. This is definitely as tough of a loss as you can get,'' Nowitzki said. ''But if a team can recover it, it's an experienced one and we definitely have a lot of older guys who have been through a lot.''
Westbrook led the Thunder with 28 points and Serge Ibaka had 22 points and five blocks. James Harden scored 19 points in his first game since sustaining a concussion when the Los Angeles Lakers' Metta World Peace hit him with an elbow last Sunday and earned a seven-game suspension.
Dallas' Jason Terry added 20 points - but none in the fourth quarter - and Marion had 17.