The Mavericks had six players in double figures for the fourth straight game. Mayo had 18 points and seven assists, and Darren Collison scored 15.
Elton Brand had 10 points and 13 rebounds for Dallas, while Serge Ibaka had 11 points and 14 boards for the Thunder.
Durant put Oklahoma City ahead 99-98 on a pair of free throws after he was fouled on a drive with 1:32 left in regulation. He hit two more after he was fouled following a rebound of a miss by Nowitzki, and Oklahoma City kept the lead until Mayo's tying 3-pointer.
"There are some things that we obviously could have done to limit him," Carlisle said of Durant. "He had a great game, and he is the best shooter on the planet."
Neither team led by more than three in the final 6 minutes of regulation and overtime.
The Mavericks, who earlier this season tied an NBA record with their 10th straight overtime loss, fell to 1-8 in overtime games this season. Two of the losses have been to the Thunder, who improved to 4-0 in overtime.
"It always seems to be a fourth-quarter game or overtime game this year," Oklahoma City coach Scott Brooks said. "Both teams did not want to lose this game."
The Mavericks trailed 87-79 when Carter hit a free throw and Nowitzki had a tip-in to start a 13-2 run that gave Dallas its first lead since the first quarter. Nowitzki's free throws gave the Mavericks the lead at 90-89 with 6:41 left.
NOTES: Nowitzki was called for a technical foul during a timeout, and Thunder C Kendrick Perkins picked up one when he got in Chris Kaman's face after Perkins was called for a foul for bumping Kaman while they were battling for a rebound. ... Mavericks F Elton Brand recorded the 400th double-double of his career Wednesday against Houston. He had 11 points and 10 rebounds. ... Durant will start in the All-Star game Feb. 17 in Houston. His coach, Brooks, won't be in charge. Brooks is ineligible to lead the Western Conference stars because he did it last year. "It was pretty cool to be able to meet some of the players and see how they are off the court," Brooks said. "Whoever gets it will have a great experience in a great city."