Reynolds powered a 1-2 pitch into the third deck in left-center field, giving the Indians their second win over the Blue Jays in as many attempts. The homer came off Sergio Santos, the sixth Toronto pitcher.
Toronto wasted a ninth-inning rally which saw Jose Bautista hit a homer to left that brought about a 2-2 tie.
After the homer by Reynolds, Joe Smith came on in the bottom of the 11th to throw a perfect inning and pick up the first save of his career. Matt Alberts recorded the final out of the 10th to get credit for the win.
Cleveland will be going after its first 3-0 start to a season in 15 years when it meets Toronto again Thursday.
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