Breunig shot 9 of 12 and grabbed seven rebounds for Montana (12-7, 7-1 Big Sky), which bounced back after its seven-game winning streak was snapped in a 63-58 loss to Idaho on Thursday.
Montana led 69-64 with 1:56 left until Venky Jois' jumper pulled the Eagles within three.
Wright answered for Montana with a reverse layin to get it back to five with 1:12 remaining, but Austin McBroom's third 3-pointer cut it to two 31 seconds later.
Jois was called for a defensive foul on Montana's next possession, and Breunig made both free throws to give Montana a four-point lead. Jois stole the ball away after the teams traded turnovers, but he was unable to make either of his free throws.
McBroom had 22 points for Eastern Washington (9-10, 3-4) and Jois added 20 points and 10 rebounds.