Also in the West, San Antonio surged into a 3-0 series lead over the Utah Jazz and the Los Angeles Clippers moved into a 2-1 lead over Memphis, while in the Eastern Conference the Indiana Pacers took a 3-1 series lead over Orlando.
In Dallas, James Harden scored 15 of his 29 points in the quarter as the Thunder completed the four-game sweep by scoring 35 points in the fourth quarter while holding Dallas to 16.
"(I was) in attack mode," Harden said. "Scotty [Thunder coach Scott Brooks] put the ball in my hands in the fourth quarter and he told me to make plays. ... It was just tremendous."
The Mavericks, just the third defending champions to be ousted in the first round, failed to score a field goal in the final 5:47.
Oklahoma City had trailed by 13 at the end of the third but sparked to life by a 12-0 run, they finally took the lead on a slam dunk by Serge Ibaka with five minutes to play.
"We didn't crumble," said Thunder All Star forward Kevin Durant, who had 24 points and 11 rebounds. "I think that's the best part of our team. We've grown in that area. We never gave up."
Dirk Nowitzki led the scoring for Dallas with 34 points but none of his team mates scored more than 16 points.
In the East, Indiana squandered a 19-point lead against the Orlando Magic but fought back in overtime to register a 101-99 victory and take a 3-1 lead in their best-of-seven series.
"We made a lot of mistakes, but we still came out of here with a win," said a relieved David West, who led the Pacers with 26 points. Indiana can clinch the first-round series with victory in Game Five on Tuesday in Indianapolis.
The Magic trailed 82-63 with 8:14 left but rallied to tie it 89-89 at the end of regulation and force overtime.
Orlando had a chance to win before the extra session but Jameer Nelson's jumper at the buzzer came up short, scraping off the front rim.
Indiana scored the first six points of the extra five-minute period but once again the Magic clawed back to tie at 99-99.
With 2.2 seconds left in overtime, Nelson fouled George Hill driving into the lane and the Pacers guard sank both free throws for a 101-99 lead.
Glen "Big Baby" Davis's desperate, fall-away jumper grazed the rim as the buzzer sounded to leave Orlando, playing without injured center Dwight Howard, on the brink of elimination.
"I'm very proud of our guys for what they gave," Orlando coach Stan Van Gundy said. "It's easy to cave in, but our guys didn't. We kept coming and coming and coming. They fought hard."
Danny Granger added 21 points for Indiana, while Hill scored the Pacers' last six points in 12 for the game.
The Magic were paced by Jason Richardson with 25 points, and Davis scored 24 and had 11 rebounds.
"It definitely was a tough game. We gave everything we had," said Richardson. "Just play for our lives now."
In the West, the San Antonio Spurs grabbed a 3-0 series lead with a 102-90 win over the Utah Jazz while the Los Angeles Clippers held off a last-minute charge by the Memphis Grizzlies for an 87-86 victory that gave the hosts a 2-1 series lead.
At Los Angeles, Memphis' Rudy Gay missed a three-pointer as the buzzer as the Clippers hung on.
Chris Paul had 24 points and 11 assists for the Clippers with Gay scoring 24 for Memphis.