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. After beating the Mavericks in the 2006 NBA Finals, Miami lost in four games to Chicago the next year.
Kevin Durant had 24 points and 11 rebounds for the Thunder, who will get a break before playing the winner of the series between the Los Angeles Lakers and Denver. The Lakers lead that Western Conference series 2-1 going into Game 4 on Sunday night in Denver.
Nowitzki had 34 points.
CLIPPERS 87, GRIZZLIES 86
LOS ANGELES (AP) — 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.
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. Eric Bledsoe missed two more free throws, Gay got a good look but missed.
Gay finished with 24 points.
Game 4 of the Western Conference series is Monday night.
PACERS 101, MAGIC 99, OT
ORLANDO, Fla. (AP) — George Hill hit a pair of free throws with 2.2 seconds left in overtime, and Indiana beat Orlando to take a 3-1 lead in the Eastern Conference series.
The Pacers won after squandering a 19-point lead in the fourth quarter. Orlando had a final chance to tie it in the closing seconds, but Glen Davis' fade away jumper bounced off the side of the rim.
David West scored 26 points, including 12 in the third quarter and four in overtime, for Indiana. Danny Granger added 21 points. Jason Richardson led Orlando with 25 points, and Davis had 24 points and 11 rebounds.
The Pacers won their third straight game and will try to close out it out Tuesday night in Indianapolis.
SPURS 102, JAZZ 90
SALT LAKE CITY (AP) — Tony Parker scored 27 points, including 16 in the fourth quarter, and San Antonio beat Utah to take a 3-0 lead in the Western Conference series.
No NBA team has ever overcome an 0-3 deficit to win a best-of-seven series. The Spurs can close it out Monday night in Salt Lake City.
Al Jefferson and Devin Harris scored 21 apiece for Utah, while Derrick Favours added 15 points, 11 rebounds and two blocks in his most extensive action of the series.