Quarterback Nick Foles was intercepted twice and the Wildcats (1-5, 0-3 Pac-12) lost two fumbles in their fifth straight loss overall and eighth straight conference loss.
Oregon State (1-4, 1-2) led 27-6 at halftime and nearly squandered it but held on to snap a six-game losing streak dating to last season.
With only a narrow 30-27 lead and 5:22 left, Oregon State went for it on fourth-and-2 -- succeeding when Mannion hit diving tight end Joe Halahuni for the touchdown.
The Beavers made a crucial stand on the other end when the Wildcats also took a chance on fourth down with two yards to go, and Dan Buckner couldn't catch Foles' pass in the end zone.
Foles completed 31 of 45 passes for 378 yards and a touchdown to Buckner, who caught eight passes for 144 yards.
Mannion, a redshirt freshman who didn't become the Beavers' official starter until the third game of the season, completed 32 of 41 passes.
The Wildcats were hurt early after starting wide receiver Juron Criner left with what appeared to be a right knee injury. Criner, ranked second in career touchdown catches for the Wildcats, has three this season.
Arizona answered with Foles' 28-yard TD pass to Buckner, but Alex Zendejas' extra-point attempt was wide left to make it 14-6.
The Beavers pulled off a fake punt to keep alive a drive that ended with Trevor Romaine's 37-yard field goal. On Arizona's ensuing drive, Foles' arm was hit and he was intercepted by Michael Doctor and the Beavers capitalized with Mannion's 3-yard scoring pass to Halahuni.
The Wildcats had one more chance in the first half, but fumbled and gave the ball back to the Beavers, who got a 40-yard field goal from Romaine.
Arizona running back Daniel Jenkins fumbled on Arizona's first drive of the second half and Beavers safety Lance Mitchell recovered, before the Beavers went up 30-6 on Romaine's 20-yard field goal.
The Wildcats had a scary moment midway through the third quarter when Foles was hit hard and stayed prone on the field for several moments while trainers attended to him. After he made his way to the sidelines, Keola Antolin ran 13 yards for a score. Foles came back and completed the two-point conversion pass to David Douglas.
The Wildcats' rally continued when Mannion was intercepted by Shaquille Richardson, who ran it back 20 yards for a touchdown. This time the two-point try failed, but Arizona was back in it at 30-20.
Oregon State missed a chance to extend its lead when James Rodgers' catch in the end zone was called back by a penalty and Romaine's 42-yard field goal attempt at the end of the third quarter went wide left.
Arizona pulled to within 30-27 early in the fourth quarter on Ka'Deem Carey's 1-yards scoring run.
The Wildcats have struggled this season with a brutal schedule, with losses to top-10 teams Oklahoma State, Stanford and Oregon, as well as their 48-41 loss last weekend at USC.
The Beavers were off to their worst start since 1996. After a season-opening overtime loss to lower-division Sacramento State, Oregon State dropped games to Wisconsin, UCLA and Arizona State.
Last season, Foles threw for 440 yards and three touchdowns against the Beavers, but Oregon State pulled out a 29-27 upset over the then-No. 9 Wildcats. Rodgers went down with a knee injury in that game that would require two surgeries and keep him out until the Beavers' third game this season.
The Beavers without true freshman Malcolm Agnew, who rushed for 223 yards in the opener, because of a hamstring injury that has forced him to miss the past five games.