The Blue Jays pulled into a 3-3 tie on Adam Lind's RBI groundout in the fourth and Alex Rios' two-run homer in the fifth.
Greg Norton's RBI double gave Tampa Bay a 3-1 lead in the top of the fifth.
Jeremy Accardo (1-1) was the loser.
Tampa Bay's Edwin Jackson gave up three earned runs and four hits in six innings with two walks and six strikeouts.
Toronto's A.J. Burnett yielded three earned runs and seven hits in seven innings with three walks and 13 strikeouts.
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