Greivis Vasquez scored a season-high 26 points for Toronto, Amir Johnson fouled out with 16, and Terrence Ross scored 11 points in the first half before leaving with a sprained left ankle.
"Our deck wasn't full and I thought it hurt us," Casey said.
Lowry fouled out as Gortat converted a three-point play with 1:45 left in the third overtime. Back-to-back turnovers by Vasquez on Toronto's next two possessions led to consecutive steals for Wall and fast-break baskets for Ariza and Webster, putting Washington up 131-127 with a minute remaining.
"We shut off the water," Webster said. "It was a tight game all the way down to the end and we were able to collect a couple of stops and convert on the offensive end."
DeRozan cut it to two with a pair of free throws, but Wall made a layup and Garrett Temple sealed it with a free throw.
Gortat made two free throws to put Washington up 118-116 with 43 seconds left in the second overtime but DeRozan tied it on a layup with 2.3 seconds left. Beal thought he'd won it at the buzzer, but his shot was waved off. Replay review upheld the call, sending it to a third OT. "Earlier in the season we probably would have dropped our heads when they told us that it didn't count and we have to play again," Ariza said. "Tonight just shows that we're growing and we're getter better."
Lowry, who missed a potential winner at the end of regulation, got the ball again in the final seconds of the first overtime but Webster blocked his driving shot.
Ross rolled his ankle when he stepped on a defender while driving to the basket at 2:15 of the second quarter. He stayed in the game to shoot his free throws, but was replaced just over a minute later and headed to the locker room for treatment. Ross did not return for the second half.
NOTES: The game had 19 ties and 15 lead changes. ... Al Harrington was called for a flagrant foul on Toronto's Tyler Hansbrough in the second quarter. ... Lowry picked up a technical foul for arguing in the final minute of the first half.