"I got into attack mode," Harden said. "I was determined to make plays."
After the Harden-fueled surge over 3 minutes got the Thunder within a point, they finally took the lead and kept it when 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.
"He beat us in individual drives, beat us in pick and rolls. He got up a head of steam and was great," Mavs coach Rick Carlisle said of Harden. "We tried everything, five or six different coverages going. We needed to be better but it was more about how good he was."
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 play the winner of the series between the Los Angeles Lakers and Denver. The Lakers lead that first-round series 2-1 going into Game 4 on Sunday night in Denver.
"This goes without saying, I'm excited we won the series," coach Scott Brooks said. "James had an incredible game. We ran pick and rolls at the angles. ... He was making plays for himself or our shooters."
Even when Harden bobbled the ball in the fourth quarter after Oklahoma City took the lead, Derek Fisher ended up with it and drove for a layup to make it 96-91. Nowitzki then had a shot that hit the rim a couple of times before falling out.
Nowitzki had 34 points, including all six of his free throws after that. But he also missed a couple of shots in that span, all that were close but not good.
With their 20-something All-Star duo of Durant and Westbrook along with the late-season addition of Fisher, who won five NBA titles with the Los Angeles Lakers, the Thunder got the franchise's first four-game playoff sweep since 1996.
That's when they were still the Seattle SuperSonics and swept the Houston Rockets in a second-round series.
"If you want to be an elite team in this league, you got to have two or three guys who can go off at any time and I just thought they had more weapons than us," Nowitzki said.
Oklahoma City finished off the Mavs without starting center Kendrick Perkins, who left the game with 4:09 left in the first quarter with a right hip strain. He had two rebounds, two assists and missed his only shot in his 8 minutes.
Jason Kidd, the Mavericks' 39-year-old point guard, had 16 points and eight assists. Jason Terry had 11 points in what might have also been his last game in Dallas.
Westbrook and Fisher had 12 points each for the Thunder.
Dallas led 86-73 on a 3-pointer by Terry before Harden scored seven in a row on a three-point play and two other baskets. Durant then made a 3-pointer, and after Nowitzki was short on a 14-footer, Harden drove for a powerful two-handed slam that got the Thunder within 86-85.
The game was tied at halftime before Nowitzki had 12 points and Kidd made three 3-pointers in the third quarter, when the Mavs scored 34 points to take an 81-68 lead.
Dallas had never been swept in a best-of-seven series. And the Mavericks hadn't lost four playoff games in a row since the 2006 NBA Finals against the Heat, when they took a 2-0 series lead before losing the rest.
Now they are the oldest team in the NBA, and vastly changed from last year's championship squad.
Still, the Mavs looked like they were ready after halftime to at least force the series back to Oklahoma City, where they opened the series with two losses by a combined four points before losing by 16 at home in Game 3 on Thursday night.
Nowitzki drove around Ibaka for a tiebreaking one-handed reverse layup less than a minute into the second half, and the lead was up to 64-54 when Shawn Marion had a slam dunk.
The closest the Thunder got the rest of the third quarter was six points, but Kidd stretched that back out with another 3-pointer.
Carlisle had talked during the off day about the Mavericks controlling their emotions after his outburst in the first quarter of Game 3. He had to be held back by an assistant coach when he charged onto the court and was pointing and screaming at an official because of what he said were three missed calls on one possession, ending with Oklahoma City scoring on what appeared to be basket interference.
Before the end of the first quarter Saturday night, Carlisle was mad again and for good reason.
Kidd had bad pass that went out of bounds, but officials missed that the ball was deflected in the air by Harden. Replays showed clearly that Carlisle had a gripe and that the loud boos were warranted.
Fisher then made it worse by hitting a 22-foot jumper when play resumed. But Vince Carter made a 3-pointer to get the Mavs within 26-24 before drawing a charge from Harden near midcourt.