Jeff Green finished with 15 points and, like Durant, had eight rebounds for the Thunder.
"It was just incredible intensity between two young teams trying to prove to each other who has a step ahead of the other," Memphis coach Lionel Hollins said. "[Both teams] showed a lot of grit tonight because nothing was going, and the referees let us play. That was good. It was like playoff basketball."
The score was tied at 84 when Green blocked O.J. Mayo's shot with 24 seconds left, but Gasol stole the ball from Durant and set the stage for the final play.
Gay took the ball at the top of the key and dribbled time off before hitting the game-winner over Durant.
The two youngest teams -- the average age for Memphis' active roster is just under 25 years old and the average age of Oklahoma City's is about 25 1/2 -- appear to be moving in the right direction. Both are over .500 as the All-Star break approaches.
"Both franchises are doing a good job of getting guys to compete every night out," Thunder coach Scott Brooks said.
Memphis built the lead to double digits in the first half behind the 3-point shooting from Conley and breakaway dunks by Gay. Conley connected on his first three shots beyond the arc. Gay had 15 points in the half, including a pair of dunks off turnovers, and Conley had 11.
But Memphis couldn't hold the lead as Durant, who struggled early -- he started 2 of 8 from the field -- keyed a second-quarter comeback for Oklahoma City.
The league's third-leading scorer hit his next four shots by taking the ball inside and getting to the foul line.
That keyed a 23-8 run to close the half, erasing a 14-point Memphis advantage and giving the Thunder a 49-48 lead at halftime. Durant had 19 for Oklahoma City.
"It was going to be a physical game," Conley said. "These are two teams trying to get to the playoffs. We knew our 14-point lead wasn't going to hold. They were going to give a hard push to get back in it."
The Thunder continued to push the defensive intensity after halftime, forcing Memphis outside its comfort zone.
That didn't allow Oklahoma City to build a significant lead, however, as the Thunder also struggled from the field.
Randolph scored 14 in the quarter, including the Grizzlies last nine points. Memphis led 72-69 going into the final period.
The teams exchanged leads in the early part of the final stanza until Memphis broke a 75-all tie with a 9-2 run, the final four coming from Randolph.
But Oklahoma City made another run, and Durant's dunk with just under 2 minutes left tied the game at 84.
"It was a great win for us as a team following the loss to New Orleans [Wednesday night]," Mayo said. "Coming here with a tough Thunder team, young like us and up and coming. It was just a great opportunity for us to get another win at home."
Hollins was promoting Randolph for the All-Star team. "Zach, frankly, deserves it," Hollins said. When asked if he would lobby for Randolph's inclusion, the Memphis coach replied: "It's something I will do. I wouldn't think that you have to, but it's part of the process." ... Thunder F/C Nick Collison returned to action after missing the last two games with a concussion. ... The Thunder remain one of only three Western Conference team with a winning record on the road. Oklahoma City is now 12-10 away from home. ... Durant has 17 straight games of at least 25 points.