Devoe Joseph had 13 points, including the last eight, and six assists as the Ducks (6-2) improved to 5-0 at home.
Chehales Tapscott led the Vikings (5-4) with 16 points. He scored 14 in the second half after foul trouble limited him to 6 minutes in the first half.
Lateef McMullen scored 14, Charles Odum 12 and Michael Harthun 10.
Portland State went on an 8-0 run, capped by a three-point play by Tapscott, to cut it to 65-59 with 4:34 left.
A 3-pointer by Harthun with 1:29 left trimmed it to 71-68. But Joseph answered with a floater off the glass and went 6-for-6 from the free throw line to finish it.
The Ducks ended the first half on a 12-5 run for a 34-27 halftime lead.