Oklahoma State (7-6) built off its comeback victory over rival Oklahoma to earn a bowl berth, dominating Washington on both sides of the ball to take a 17-point halftime lead.
The Cowboys kept the Huskies' vaunted front seven from harassing Rudolph most of the night and the freshman was poised in his third career start, shrugging off three turnovers to hit 17 of 26 passes.
Defensive tackle James Castleman even got in on the offensive action with a 1-yard touchdown run and 48-yard reception.
Washington (8-6) stagnated offensively in the first half before finding a rhythm, but couldn't overcome the early deficit to close out coach Chris Petersen's first season with a loss.
John Ross scored on a 96-yard kickoff return and Cyler Miles threw for 268 yards and a touchdown, but had an interception on Washington's last-ditch drive.
The Cowboys pulled off a last-minute comeback to earn a spot in the Cactus Bowl, scoring two touchdowns in the final 8 minutes to knock off Oklahoma in overtime.
Tyreek Hill had the big play in that game, scoring on a 92-yard punt return with 45 seconds left, but he was dismissed from the team last month after being arrested on charges of choking and punching his pregnant girlfriend.
That left Oklahoma State without its most dangerous threat against a Washington defense that has three first-team All-Americans.
The Cowboys didn't seem to mind.
They had no trouble against Washington's ferocious front seven on their opening drive, confidently converting a midfield fourth-and-1 while marching 84 yards for a score. The Cowboys capped it by lining up Castleman in the shotgun and the 300-pounder rumbled in on a 1-yard dive off left tackle.
Rudolph turned it over on the next two drives, losing a fumble when he was sacked, then on a one-handed interception by Budda Baker.
The freshman kept his poise, though. He caught a pass from receiver Brandon Sheperd on a trick play to set up a 28-yard touchdown pass to James Washington, who one-upped Baker with a one-handed catch in the end zone.
The Sheperd-Rudolph connection worked again just before the half, this time in reverse: Rudolph on the throw, Sheperd on the catch for a 47-yard touchdown that put the Cowboys up 24-0.
Washington had 113 total yards in the half.
The Huskies finally showed signs of life on their opening drive of the third quarter, cutting into Oklahoma State's lead on Jaydon Mickens' 31-yard reverse.
Washington got a bad break when a punt hit one of its players and Oklahoma State recovered, but held the Cowboys to Ben Grogan's 27-yard field goal. Ross took the ensuing kickoff up the middle, made a couple of jukes and raced off to a 96-yard touchdown that cut the Cowboys' lead to 27-14.
Miles followed with a 16-yard touchdown pass to Mickens, trimming the lead to 30-2 with 3 1-2 minutes left, but Castleman caught a pass and rumbled down the sideline for a 48-yard reception that all but killed the Huskies' chances.
UW loses Cactus Bowl 30-22 to Oklahoma State
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