The Eagles (23-8, 14-4) closed the game with the final 10 points after Weber State's Joel Bolomboy opened the overtime scoring with a jumper at 71-69.
Eastern Washington shares the conference title with Montana, though the Grizzlies win the tiebreaker for the No. 1 seed and the right to host the Big Sky tournament.
Weber State (13-16, 8-10) jumped ahead 37-18 late in the first half. But the Eagles ended the half on a 9-2 run to get within 12.
Richaud Gittens had 22 points to lead the Wildcats.