The Huskies rallied from a 15-point deficit in the second half to eliminate the No. 5 seed in the East Region and complete a dismal day for the Big East Conference to open the national championship tournament.
Marquette joined Notre Dame and Georgetown as Big East teams to be eliminated in the first round. The only Big East winner Thursday was Villanova and the Wildcats had to go into overtime to survive against Robert Morris.
Four more Big East teams -- West Virginia, Pittsburgh, Syracuse and Louisville -- will be in action Friday.
The teams were locked in a 78-78 deadlock when Washington's Matthew Bryan-Amaning turned it over with 1:38 to play. Jimmy Butler, however, lost the ball for Marquette with 1:02 to go.
Washington's Isaiah Thomas missed a 3-point attempt with 37 seconds left, but Pondexter grabbed the offensive rebound.
The Huskies ran the shot clock down before Pondexter headed into the lane for his game-winning shot. Lazar Hayward missed a 3-point try just before the buzzer for the Golden Eagles.
Thomas led Washington (25-9) with 19 points and Pondexter had 18. Washington hit 54 percent of its shots and made 9-of-14 from 3-point range.
Marquette (22-12) was led by Hayward with 20 points.