Toronto trailed 2-0 and 4-3 before its 10th comeback win this season and third of the series completed a three-game series sweep.
Danny Jansen, hitting .095, led off the ninth with a single off Will Smith (0-3). Marcus Semien singled, and Bichette doubled to the gap in right-center for a 6-4 lead.
Bichette drove in three runs on two hits. Cavan Biggio knocked out Smith with his second double of the game to drive in another run.
Travis Bergen (1-0) pitched a scoreless eighth. Jordan Romano struck out the side in the ninth.
Acuña led off the game with his major league-high 12th homer, then got hurt while trying to beat out a grounder to third base.