With the score tied 4-4 in the 12th, Miguel Cabrera drew a leadoff walk from David Phelps (0-1), went to second on an out and then scored when Young lined a pitch that eluded Yankees right-fielder Nick Swisher.
Don Kelly came in to run for Young and went to third when Jhonny Peralta scorched a grounder. New York shortstop Derek Jeter stumbled while fielding the play, breaking his left ankle. He is out for the rest of the post-season.
The next batter, Andy Dirks, followed with another infield hit that sent Kelly home with an insurance run.
Drew Smyly (1-0) fired two scoreless innings to earn the win, which gave the Tigers a 1-0 lead in the best-of-seven ALCS.
Young finished 3-for-6 with three RBI and a solo homer.
Suzuki collected four hits for the Yankees, who will host Game 2 Sunday.