Bautista's blast in the first inning staked the Blue Jays to a quick 2-0 lead but Josh Reddick responded with a two-run clout of his own in the top of the second to knot the score.
Toronto took the lead for good in the next inning when Brett Lawrie struck out but reached first on a wild pitch and later came around to score on a Jose Reyes fielder's choice groundout.
The Blue Jays capitalized on an error by Oakland third baseman Josh Donaldson in the third when Colby Rasmus singled home Bautista, then made it 5-3 when Reyes socked a solo homer in the seventh.
Mark Buehrle (8-7) got the win, surrendering three runs on seven hits over 5 1/3, walking two and striking out five.
Casey Janssen picked up his 21st save despite allowing another Reddick homer in the ninth as the Blue Jays rebounded from a 14-6 loss in Friday's four-game series opener.
Reddick's two homers gave him five in two games for Oakland, which came into the contest tied with Texas for the American League West lead.
Sonny Gray (0-1) absorbed the loss in his major league debut, allowing four runs (two earned) on four hits in six innings.
Celebrity Families of 2014 [PHOTOS]