The Bobcats (12-8, 4-3 Big Sky) trailed 44-27 at the break but rallied in the second half. They went on a 12-2 run capped by a Branden Johnson 3-pointer with 8:41 remaining to take their first lead of the game.
Down 72-69 with 13 seconds remaining, the Eagles (8-14, 3-5) had a chance to tie the game. But Mbunga, who finished with 17 points, blocked a jumper by Trey Gross and was fouled. Mbunga's free throw put Montana ahead by four with 12 seconds remaining.
Adris DeLeon led Eastern Washington with 22 points, although he turned the ball over nine times. Matthew Brunell added 13 points.