The Thunder trailed by 13 points with 9:44 left before Harden scored seven in a row, and nine in a 12-0 run over the next 3 minutes.
Oklahoma City finally took the lead, and kept it, after Russell Westbrook stole the ball from Dirk Nowitzki and passed to Serge Ibaka for a two-handed slam that made it 92-91 with 5:17 left.
Dallas is the second defending champion in five years to be swept in the first round.
CLIPPERS 87, GRIZZLIES 86
In Los Angeles, Chris Paul had 24 points and 11 assists and high-flying Blake Griffin added 17 points for Los Angeles, which beat Memphis only after Rudy Gay missed a jumper just before the buzzer.
The Clippers won their first home playoff game in six seasons to take a 2-1 series lead in the Western Conference playoffs.
Paul hit a fadeaway jumper with 2:02 left for an 82-80 lead. On the next possession he had a no-look bounce pass to Griffin coming in off the baseline for a monster slam.
Trailing 86-80 after two free throws by Paul, Gay hit a 3-pointer with 12.9 seconds left, Memphis’ first field goal since 7:10.
After Los Angeles missed three of four free throws, Gay hit another 3-pointer with 8.9 seconds.
PACERS 101, MAGIC 99
In Orlando, Fla., George Hill hit a pair of free throws with 2.2 seconds left in overtime to help Indiana survive squandering a 19-point fourth quarter lead and beat Orlando to take a 3-1 series lead.
David West scored 26 points, including 12 in the third quarter and four in overtime for Indiana. Danny Granger added 21 points.
The Pacers won their third consecutive game and will try to close out the series on Tuesday night in Indianapolis.