Shuck went into the left-field corner to track down a shot by Bautista in the fourth inning. He leaped above the short wall, snagging the ball before tumbling into the stands.
Fans gave him a pat on the back as Shuck scrambled back onto the field.
Angels teammates in the dugout gave him a tip of the cap.
Bautista stood near first base, seemingly mesmerized by the catch.
"You don't play many baseball games where there's a catch like that," said fellow Angels rookie outfielder Kole Calhoun, who happened to hit what proved to be the game-winning, two-run home run in the eighth inning.