Deon McIntosh had 147 yards rushing and a touchdown as the Cougars amassed 456 total yards.
Nick Rolovich got a win in his first game as coach at Washington State, which was without running back Max Borghi. The junior has 28 career touchdowns, including 16 last season.
The Beavers rallied late behind quarterback Tristan Gebbia and cut the lead to 31-28 with 2:39 remaining on Jermar Jefferson’s 15-yard run, and Gebbia's 2-point conversion pass to Trevon Bradford.
But Washington State recovered the on-side kick and scored on the next play — a 44-yard touchdown run by Travell Harris.