Bautista's homer leading off the bottom of the ninth -- the second of his two solo shots -- tied the contest 3-3.
Then in the 10th, the Blue Jays loaded the bases with one against Rays relievers Joel Peralta and Cesar Ramos (1-1), and Bautista followed by slicing a hit into right against Kyle Farnsworth, scoring Colby Rasmus with the winning run.
Bautista finished 4-for-4 with all four RBI as the Blue Jays claimed the rubber match of their three-game series, winning a set against Tampa Bay for the first time in 16 meetings.
Aaron Loup (2-3) earned the decision after tossing a scoreless top of the 10th.
Rays starter Jeremy Hellickson surrendered two runs on four hits over eight full innings.