Trailing 3-2 entering the frame, the Tigers struck for three runs to stun the Angels.
Prince Fielder collected a one-out single against Garrett Richards (3-3), and one out later Andy Dirks sent him to third with a base hit.
That brought up Peralta, who scorched a 1-1 pitch past diving Angels third baseman Alberto Callaspo and into the left field corner, scoring both runners.
Octavio Dotel (4-2) earned the victory with two shutout relief frames for the second-place Tigers, who remained 2 1/2 games behind the American League Central-leading Chicago White Sox.
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