The Mavericks beat the top-seeded Thunder 4-2 in the best-of-seven conference semi-final series to reach the conference finals for the second time in three years.
They'll face either the defending champion Denver Nuggets or the Minnesota Timberwolves, who faced a deciding game seven in their series on Sunday.
"Being down 17 in a closeout game isn't a position you want to be in," said Dallas star Kyrie Irving. "We had to respond the way we've responded all season, just playing hardnosed basketball on the defensive end, getting out in transition and just trusting that our pace would get us back in the game.
"It definitely feels good to get the series done."
Doncic scored 29 points with 10 rebounds and 10 assists. Irving and Derrick Jones Jr. scored 22 points apiece and Dereck Lively added 12 off the bench for the Mavs.
Washington scored all nine of his points in the fourth quarter - including two free-throws with 2.5 seconds remaining that lifted the Mavs to victory.
"I think he was just waiting for his moment," Irving said.
It came after a controversial call in the waning seconds with the Mavs down 116-115. Doncic drove into the lane then passed to Washington in the corner, but Washington was fouled on his three-point attempt by Thunder star Shai Gilgeous-Alexander.
Oklahoma City challenged the call but it stood. Washington made the first two free throws before intentionally missing the third, the Thunder grabbing the rebound but unable to make a shot from beyond halfcourt.
"If I had the moment back I wouldn't have fouled him, let him make or miss the shot," Gilgeous-Alexander said. "Basketball - you win some, you lose some. You make mistakes."
Gilgeous-Alexander, like Doncic a finalist for the Most Valuable Player award won by Denver's Nikola Jokic, scored 36 points to lead the Thunder, who led by 16 at halftime and pushed the advantage to 17 early in the third before the Mavericks stormed back in front of a frenzied home crowd.
A three-pointer by Washington tied it at 105-105 with 4:11 remaining and they traded the lead three times from there, Thunder rookie Chet Holmgren throwing down a dunk to put Oklahoma City up 116-115 with 20.4 seconds left.
Amazing effort
Facing elimination, the Thunder burst out of the gate and led by seven after one quarter.
Doncic gave the Mavs their first lead of the game with less than five minutes left in the second quarter.
The Thunder responded with a vengeance as back-to-back dunks from Chet Holmgren and Jalen Williams restored their lead. Oklahoma City finished the second quarter on a 24-6 run to lead 64-48 at halftime.
With Doncic and Irving leading the way the Mavs clawed back in the third, out-scoring the Thunder 35-26 in the period.
"The whole team is amazing," Doncic said. "Amazing comeback, amazing effort. This team is special."
Thunder coach Mark Daigneault was full of praise for his young team. Oklahoma City's starting five have an average age of 23, but matched the Nuggets for best record in the West and swept the New Orleans Pelicans in the first round of the playoffs.
"I've said all year this has been a total pleasure," he said. "It's really sad for that to finish."
