Dallas had been embarrassed 108-70 in the opener on Saturday, but the Mavericks bounced back and held Oklahoma City to 33.7 percent shooting on Monday.
"I'm very proud of our guys and the way they responded after one of the most disappointing games in franchise history," Dallas coach Rick Carlisle said. "It's a group with a lot of pride, and obviously, a lot of resilience."
In the postgame news conference after the Game 1 loss, Carlisle defiantly stated that the loss was not significant, and that it was just one game. His team bought it, and, even goes home for Thursday night's Game 3 with a chance to take the lead in the series.
Raymond Felton had 21 points and 11 rebounds and Dirk Nowitzki added 17 points for the Mavericks.
Deron Williams, declared doubtful on Sunday with a left abdominal strain, scored 13 points for Dallas, 11 in the game's first 5 minutes.
"This wouldn't be possible if Deron Williams hadn't given it a shot," Carlisle said. "He got us off to a good solid start — actually better than a solid start, he got us off to a very good start."
Kevin Durant scored 21 points for Oklahoma City, but he made just 7 of 33 shots in the worst postseason shooting performance, both by percentage and number of misses, of his career. Durant's 26 misses were the most he's had in 716 career games, including the regular-season and playoffs.
"It was a bad shooting night for me," Durant said. "It's part of it. I wish it didn't happen tonight, but it's a part of it. I got some great looks all night and I just didn't knock them down. It was just one of those nights."
The Mavericks said they did a good job of being physical with Durant and disrupting his rhythm.
Dallas led 85-84 with 7.1 seconds left when Felton missed two free throws. Durant got the rebound of the second, but his shot to try to win the game was blocked by Justin Anderson. Russell Westbrook rebounded and missed, then Adams rebounded Westbrook's miss and made a basket, but the ball was in his hand as time expired.
Westbrook finished with 19 points and 14 rebounds and Serge Ibaka added 12 points for the Thunder.
Dallas led 69-68 before the Thunder went on an 8-0 run, highlighted by a dunk by Durant and a 3-pointer by Ibaka, to take a 76-69 lead.
Felton's layup with 28.7 seconds left put the Mavericks up 83-81. After Durant missed a short jumper and a 3-pointer, Wesley Matthews made a transition layup to push the lead to four with 14.4 seconds remaining.
Durant came back with a 3-pointer to trim Dallas' lead to 85-84 with 9.5 seconds to play, setting up the frantic finish.
"Look, Game 1 of a playoff series, you're going to get hit with a haymaker at the beginning, and they're a great first-quarter team," Carlisle said. "We just didn't recover from that haymaker in Game 1. In Game 2, we did a much better job. Our disposition was stronger, our posture was great and we were very together."
Felton on the missed free throws: "I'm still sick. Even though we got the win, I'm still sick. I don't miss free throws like that, when they come down the clutch. When we get in the gym, I'll take 500 free throws if I need to before the next game."
Westbrook's 14 rebounds were a career playoff high. It was the seventh time in 65 career playoff games that he had at least 10 rebounds.
Dallas' Charlie Villanueva and Anderson interrupted Westbrook's pregame dance routine with Cam Payne. Villanueva stood between the two, and Westbrook shoved him and continued to dance. Anderson stepped behind Westbrook, who nudged him out of the way with his elbow.
Mavericks: G J.J. Barea (right groin strain) and F David Lee (right plantar fascia injury) did not play. ... Dallas shot 55.6 percent in the first quarter. ... Nowitzki's jumper rattled in with 2.8 seconds left in the first half to give the Mavericks a 45-43 lead.
Thunder: C Nazr Mohammed (right calf strain) sat out. ... F Mitch McGary (undisclosed personal reasons) wasn't with the team. He hasn't played for the Thunder since March 18. ... Oklahoma City made 5 of 16 3-point attempts in the first half and 7 of 32 overall.
Follow Cliff Brunt on Twitter: www.twitter.com/CliffBruntAP.