The A's intentionally walked Prince Fielder to load the bases and Kelly followed by hitting a deep fly ball to right, allowing Infante to score the winning run without a throw.
Cabrera finished 3-for-5 and Delmon Young drove in a run for the Tigers, who grabbed a commanding lead in the best-of-five American League Division Series.
Al Alburquerque (1-0) earned the victory after retiring Yoenis Cespedes in the top of ninth to get out of a two-on, two-out jam.
Josh Reddick socked a homer and Chris Pennington went 2-for-3 with an RBI for the AL West champion A's.
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