The Tigers' only lead came after Austin Jackson's home run to lead off the game. The Red Sox immediately went ahead 2-1 in the bottom of the first when Carl Crawford had an RBI-single and then scored on a groundout by Dustin Pedroia.
Miguel Cabrera tied it with an RBI-single in the third, then Dustin Pedroia put Boston up 4-2 with a two-run home run in the sixth.
An Alex Avila double scored Brennan Boesch in the seventh inning, but Jacoby Ellsbury had an RBI-single in the seventh for the Red Sox and Will Middlebrooks' two-run home run in the eighth made it 7-3. The Tigers wouldn't get any closer.
Max Scherzer (10-6) pitched 6 1/3 innings, giving up seven hits, five runs and striking out nine. He was replced by Phil Coke in the seventh.
Clay Buchholz (9-2) pitched eight innings and gave up five hits, three runs and struck out four.
Game 2 of the series is slated for Tuesday at 7:10 p.m. ET at Fenway Park.
For more on the series, stay locked with this StoryStream. For more on the Tigers, visit Bless You Boys. For the Boston perspective, just head to Over The Monster. And for more MLB news and analysis, head over to Baseball Nation.