Allen started in Gay's place and scored a season-high 27 while harassing NBA scoring leader Kevin Durant, and the Memphis Grizzlies beat the Oklahoma City Thunder 105-101 in overtime Tuesday night.
Allen had five of the Grizzlies' 11 steals and prevented Durant from having much of an impact in overtime as Memphis won on the road in the second game of a back-to-back despite being without two key players.
"The guy was an all-pro all night on both ends of the floor - 27 points and he made Kevin work for every shot. I thought he won the game for them," Oklahoma City coach Scott Brooks said.
"Certain guys in this league compete every possession, and he's one of them. He competes every possession, and I love guys that hate getting scored on."
Durant still had 31 points and 11 rebounds, but got off just one shot in overtime and also had a key turnover in the final 20 seconds with the Thunder down by three.
"He was just an unbelievable player on defense," Grizzlies coach Lionel Hollins said of Allen. "Durant is a great player and he's going to score. I thought Tony kept him from going off and getting 40 on us."
Zach Randolph had 31 points and 14 rebounds, and all five Memphis starters scored in double figures. Sam Young scored 14, Mike Conley had 13 and Marc Gasol finished with 12.
Gay sat out with a sprained big right toe, and the Grizzlies were already without O.J. Mayo because of a league-imposed 10-game suspension.
"Having Rudy out and O.J. not here and guys banged up here and there but to still come out and beat a good team like Oklahoma City, it shows a lot about our team," said Conley, who put Memphis ahead to stay with a free throw with 2:55 left in overtime.
Young's baseline jumper bumped the lead to 100-97 and Russell Westbrook missed two critical free throws before Durant made two to get Oklahoma City back within one. Randolph then converted inside for a layup with 28 seconds left to make it 102-99.
Durant tripped while trying a crossover dribble at the other end, and the Thunder were forced to foul Conley. He went 1 for 2 but it was enough to keep Oklahoma City from getting a shot at the tie.
After Jeff Green tipped in Serge Ibaka's missed 3-pointer, Conley hit two more free throws to ice it with 5.4 seconds left.
Oklahoma City made just one of its first eight shots in overtime, with Durant connecting on his only attempt in that span. But when he did get the ball late, he couldn't bail out the Thunder.
"Tony Allen did a great job making sure that Durant didn't get too many touches, making sure that if he did get touches, he was right there in his face and made him take a tough shot every time," Young said.
Westbrook added 21 points and 11 assists but also tied his season-high with eight turnovers for Oklahoma City, which lost for the first time in six overtime games this season.
Memphis, which leads the league in steals and forced turnovers, had 23 takeaways that produced 31 points. Allen was the catalyst for it all.
"I just played hard, and that's it. That's all," Allen said. "It was a team win, and I was able to take advantage of my opportunity."
James Harden scored 13 and was the only other player in double figures for the Thunder, who lost despite a 58-36 rebounding advantage.
Durant's jumper from the left wing put the Thunder up 95-92 with 1:43 left in regulation.
After a Westbrook miss, Allen raced down for a fast-break layup that led to a tying three-point play. The Grizzlies had a chance to go back ahead, but Conley traveled with 21.7 seconds left in regulation.
Westbrook had the ball tipped away before airballing a 3-pointer from the right wing, and Harden's acrobatic putback at the buzzer didn't fall.
"It was a must-win game. It was a game that we needed just on the simple fact that we just lost two and we didn't want this game to translate to a three-, four-, five-game losing streak. We had to dig down," Young said.
Oklahoma City gave up its fewest first-half points in 22 games, having allowed 55.4 points on average during that stretch, and led 54-44 at the break.
Allen's putback of a Greivis Vasquez miss put the Grizzlies ahead in the final minute of the third quarter, and Randolph added two free throws to make it 74-71 Memphis after three quarters.
NOTES: Durant was selected as a participant in the 3-point shootout. He won the H-O-R-S-E competition the last two years, but there won't be one this year. "Hopefully I can have a good time and hopefully I come back with a win," Durant said. Coach Scott Brooks went a step further. "He can win it. I guarantee a win." ... The Thunder weren't sure whether a rib injury would keep Ibaka, a participant in the NBA's slam dunk contest next weekend, out until after he arrived at the arena. ... Memphis plays 17 of its last 28 games at home.