Masterson (1-0) helped spoil the Blue Jays' home opener by limiting his opponents to just one run on three hits over six innings, overcoming four walks while striking out five.
Chris Perez fired a scoreless ninth to record his first save.
Drew Stubbs and Lonnie Chisenhall each provided an RBI for the Indians, who finished with a 68-94 mark last season.
Blue Jays catcher J.P. Arencibia had trouble corralling Dickey's knuckleball -- he was charged with three passed balls.
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