The Titans were up by 13 less than five minutes into the game but watched as the Huskies dwindled their lead down little by little, cutting it down to single digits, 52-44, with 14:31 left in the second half.
The Huskies continued to chip away at the lead, tying the game with 4:23 remaining on a Desmond Simmons jumper. Aziz N'Diaye then scored on a dunk, giving the Huskies their first lead with 2:57 left, 67-65.
Tied at 72 with three seconds left, the Huskies' C.J. Wilcox was fouled and buried two free throws to win the game.
Wilcox finished with 21 points but was held to just 7-for-21 shooting. Simmons put up a double-double with 14 points and 18 rebounds.
The Titans were led by D.J. Seeley's 24 points and five steals but he was responsible for six of the team's 13 turnovers.
Washington improved to 4-3 while Fullerton fell to 3-4.