Durant missed a jumper just inside the 3-point line at the regulation buzzer.
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.
Nowitzki finished with 18 points after starting 1 of 11 from the field. He scored 12 in the fourth quarter, salvaging his 10th straight double-figure game after scoring in single digits the first four games following his return from missing 27 games after right knee surgery.
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.
Neither team led by more than three in the final 6 minutes of regulation and overtime.
The Mavericks were within 78-72 when Mayo stole a pass from Durant but missed a layup in the final seconds of the third quarter. Durant quickly had the ball back in his hands and hit a 3-pointer for an 81-72 lead with 2.8 seconds left.