Bautista's first blast, a solo shot, came in the sixth and gave Toronto a 2-0 lead, but the Red Sox came back to tie it in the seventh on a two-run single by Shane Victorino.
Aaron Lind went 3-for-4 with an RBI for Toronto, which rebounded from two straight losses against American League East-leading Boston.
Steve Delabar (5-1) earned the win with 1 2/3 scoreless relief innings.
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