David Cooper and Adam Loewen both homered in the seventh off Baltimore starter Tommy Hunter (3-4), with Loewen's solo blast -- the first for the former Orioles hurler -- to straightaway center pulling Toronto even.
Mike McCoy then doubled and Eric Thames singled before Willie Eyre replaced Hunter and surrendered the sac fly to Bautista.
"I just tried to keep it rolling," McCoy said.
Making his first start in over three years, Toronto's Dustin McGowan gave up four runs on three hits and five walks in three-plus innings. The 29-year-old right-hander had been sidelined with shoulder and knee problems.
Joel Carreno (1-0) picked up his first win in the majors with a scoreless inning of relief.
Hunter was tagged for six runs -- four earned -- on nine hits in 6 1/3 frames.
"I've got to figure out a way to finish a ballgame," Hunter said. "I've got to be smarter about situations."
McGowan struggled with his command in the first inning, issuing two walks and uncorking a wild pitch. Vladimir Guerrero gave Baltimore an early lead with a sac fly.
The Blue Jays countered with two runs in the bottom of the frame. Thames and Bautista hit consecutive singles to score McCoy, who reached on an error to begin the first. A pair of groundouts by Adam Lind and Brett Lawrie plated Thames.
Baltimore loaded the bases in the second, and Matt Angle tied the game by stroking an RBI single to right field. But Lind put the Blue Jays back on top in the third with a two-out single that scored McCoy.
Nick Markakis, though, put the O's in front, 4-3, with a two-run single off Carlos Villanueva in the fourth. Villanueva had relieved McGowan, who was lifted after walking Chris Davis and Nolan Reimold. Villanueva retired the first two batters he faced before intentionally walking J.J. Hardy to load the bases. Markakis followed with a line drive to right.
Angle scored on a fielder's choice by Matt Wieters in the sixth to make it 5-3.
Toronto won its seventh straight series from the Orioles...Bautista upped his RBI total this year to 98...McGowan went 0-4 with a 2.80 ERA in 12 combined rehab starts between Class A Dunedin and Double-A New Hampshire prior to being activated from the 60-day disabled list last Monday. He last started in the majors on July 8, 2008, taking a no-decision in a 7-6 win over the Orioles...Loewen pitched for Baltimore from 2006-08, going 8-8 with a 5.38 ERA in 35 games (29 starts).