The Tigers had a 3-0 lead through three, but Boston put together a big fourth inning after the first two batters were retired.
Detroit tied it in the seventh, but Gonzalez put Boston back in front in the bottom of the inning with an RBI double and Youkilis hit a homer in the eighth to close out the scoring.
Matt Albers (1-0) came on for Boston in the seventh and gave up a single, a run-scoring double and an intentional walk before recording the final out of the inning. Nevertheless, he was credited with the win.
Octavio Dotel (1-2) gave up Boston's go-ahead run in the seventh to take the loss.
The Red Sox won their third in a row and the Tigers have dropped three straight.
Celebrity Families of 2014 [PHOTOS]