DeMar DeRozan had 34 points for the Raptors (32-26), while Greivis Vasquez had a season-high 26 points and eight assists from off the bench. Kyle Lowry added 18 points to go with 10 assists and nine rebounds before fouling out.
Wall picked off Vasquez on back-to-back possessions with the game tied 127-127 in the third overtime, leading to four quick points by the Wizards (30-28) to give Washington a four-point lead.
DeRozan would get the Raptors within two with a pair of free throws, but a layup from Wall extended Washington's advantage to four with 29 seconds on the clock.
DeRozan missed a jumper with 24 seconds remaining and Garrett Temple clinched the victory on a free throw to put Washington up 134-129 with 21 seconds to go.
Amir Johnson, Patrick Patterson and Lowry fouled out for the Raptors. Trevor Ariza and Gortat fouled out for the Wizards.
In a second overtime session with as many turnovers as field goals, Gortat calmly sank two free throws to put the Wizards ahead by two with 43 seconds remaining. DeRozan tied the game with 2.5 seconds remaining.
Bradley Beal scored as the buzzer sounded, but the bucket was waved off. Reviews confirmed that Beal did not get the shot off in time.
Ahead by two with 30 seconds remaining in overtime, Vasquez lost the ball to Wall who tied the game at 114 with 23 seconds remaining. Wall would block Lowry's layup attempt as time expired to force a second overtime.
Back-to-back makes from Vasquez closed out Toronto's scoring in regulation. Gortat tied the game at 106 with 5.2 seconds remaining and a layup by Lowry missed at the buzzer, forcing overtime.
DeRozan and Lowry combined to score 22 of Toronto's 24 points in the third quarter. The Raptors trailed Washington 83-78 going into the fourth.
After leading by six at the end of the first quarter, the Raptors allowed Washington to close the gap. With 2:15 remaining in the second quarter, Terrence Ross stepped on the foot of a Wizard's player and rolled his left ankle while being fouled on a layup attempt. He stayed in the game to make the free throws, but left with a little less than a minute remaining in the half and did not return.
Toronto closed the half with a Lowry technical followed up by a DeRozan turnover. Washington took a 57-54 advantage into the break.
It was the second missed game for Washington's Nene who is out with a sprained MCL.