Rutschman flied out four times and stranded a combined eight runners in his previous four at-bats before coming up with two on against Blake Workman (6-3). He quickly gave Oregon State its first lead of the game by hitting a 1-1 fastball up the middle and scoring Trevor Larnach from second.
The Beavers (55-4) will play the winner of LSU-Florida State on Monday night. The Titans (39-23) will play the loser of LSU-Florida State in an elimination game on Monday afternoon.
Rutschman's clutch hit gave Oregon State its 22nd straight win in a game it trailed 5-1 through four innings. It also occurred shortly after KJ Harrison was robbed of an extra-base hit by center fielder Scott Hurst's leaping catch.
The catcher got the chance to deliver the hit after Jack Anderson was hit by a pitch. Anderson was 3-for-3 and reached base in all five plate appearances.
Jake Muholland (7-1) threw 4 1/3 scoreless innings and Drew Rasmussen retired the side in the ninth for the save. Oregon State's bullpen came through after undefeated starter Jake Thompson allowed five runs and three hits in 3 2/3 innings.
Oregon State did little against Titans starter Connor Seabold, who allowed one run and six hits in five innings.
The comeback started with a sacrifice fly by Nick Madrigal off Colton Eastman and Larnach hit a two-run single to make it a one-run game. The Beavers tied the game at 5-5 on a single by Anderson.
Timmy Richards hit a three-run homer in the first off Thompson and Chris Hudgins hit a two-run single in the fourth to put the Titans up 5-1.