David Robertson sealed off an impressive outing by Brandon McCarthy, who pitched out of a bases-loaded jam in the second inning and allowed just one run in six innings.
The highlight of the game came in the bottom of the third, when Ezequiel Carrera robbed Jacoby Ellsbury of a few RBIs with a diving catch on the warning track. That play kept the Tigers within striking distance, but the big bats couldn't string together enough hits against McCarthy and the Yankees bullpen.
The Yankees, who are tied with Toronto in the loss column, trail the Blue Jays by just one game for the second American League Wild Card. Detroit's lead over Kansas City in the AL Central slips to 4.5 games after the loss.
The Yankees and Tigers will face off again tomorrow at 7 p.m. in the second game of four. David Price will take the mound for the first time as a Tiger, and he will face Hiroki Kuroda.