DaShaun Wiggins scored 18 points while Gary Winston added 11 for the fifth- seeded Vikings (17-13), who will played second-seeded North Dakota on Friday.
Kareem Jamar tallied 20 points and eight rebounds for the fourth-seeded Grizzlies (17-13). Jordan Gregory chipped in 18 points and Michael Weisner finished with 10 and six boards off the bench before fouling out.
Montana shot 46.4 percent from the field in the first period as it led 28-26 at the half. Portland State made just eight field goals and connected on 32 percent of its shot attempts.
The Vikings got hot in the second frame as they drained 57.1 percent of their field goal attempts and went 18-of-21 at the free-throw line. With 7:40 in the half Gary Winston made a layup to take the lead for good as PSU went up 45-44. The Vikings went on a 7-2 to create some room that they maintained until the end of the game.
In a game that featured seven ties and eight lead changes, the Vikings took full advantage of their 26-12 scoring advantage at the free-throw line.