DeShaun Wiggins scored 12 points, Tiegbe Bamba 10, and the Vikings (7-4, 1-0) were outshot 46.9 percent to 37.3 percent, but hit 28 of 39 free throws.
The lead changed hands six times before Southern Utah pulled ahead 20-13 on a free throw by A.J. Hess. Portland State used a 12-2 run to lead 25-22, then Winston hit back-to-back 3-pointers and the Vikings led 40-36 at halftime.
Portland State led 57-48 in the second half after a jumper by Brandon Cataldo, but the Thunderbirds pulled within a point, 64-63, after a jumper by Casey Oliverson with 2:50 left. The Vikings scored seven free throws in the final 2:16 to seal the win.
Trey Kennedy led the Thunderbirds (3-9, 0-1) with 16, Hess had 13 and Oliverson 12.