Trailing 5-1 entering the fourth, Oakland struck for six runs to wrest control of the final regular-season contest of the year, which decided the American League West championship.
Derek Holland (12-7) relieved and recorded two outs, but Crisp then sliced a fly ball that landed just inside the right field line, forging a 5-5 tie.
Brandon Moss knocked in three runs and Evan Scribner (2-0) tossed three scoreless relief innings to earn the win.
The Rangers will face either the New York Yankees or Baltimore Orioles in a one-game, play-in series Friday.
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