Boesch connected for a two-run shot while Ramon Santiago and Ryan Raburn each ended with two hits and an RBI for the Tigers, who salvaged a win in the final game of their season-opening series at Yankee Stadium.
Max Scherzer (1-0) picked up the win despite allowing six runs on nine hits over five innings, issuing two walks and striking out six.
Jose Valverde collected his first save with a scoreless ninth for the Tigers.
Mark Teixeira blasted his third homer in three games and Jorge Posada added a pair of two-run blasts for New York.
The Yankees' Phil Hughes (0-1) was touched for five runs on five hits and two walks and one strikeout.