Oregon State went up 24-14 with 11:14 left in the game after Mannion connected with Obum Gwachum for a 58-yard pass that set up a Stevenson touchdown.
Montana fumbled on the next drive deep in Husky territory and Stevenson scored again to put the Beavers up by 17.
Price relieved Montana in the fourth quarter and led a 10-play, 58-yard touchdown drive to shave Oregon State's lead to 31-21.
But Price was intercepted after the Huskies recovered an Oregon State fumble during kickoff and the Beavers went 99 yards for a touchdown.
Nick Montana was 11 of 21 passing for 79 yards for the Huskies (6-5, 4-4) in his first career start.
Beavs toss aside Huskies 38-21
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