The Huskies were down by 13 less than five minutes into the game but cut the lead down little by little, bringing it down to single digits, 52-44, with 14:31 left in the second half.
The Huskies tied the game with 4:23 remaining on a Desmond Simmons jumper. Aziz N'Diaye scored on a dunk less than two minutes later, giving the Huskies their first lead, 67-65, with 2:57 left.
Tied at 72, the Huskies' C.J. Wilcox was fouled with three seconds left. He buried both freebies and the Huskies escaped with the win.
Wilcox finished with 21 points but shot only 7-for-21 from the field. Simmons was huge with a double-double of 14 points and 18 rebounds.
The Titans were led by D.J. Seeley's 24 points and five steals but he turned the ball over six times.
Washington improved to 4-3 while Fullerton fell to 3-4.