After blowing a 3-1 lead in the eighth by giving up back-to-back homers to Brennan Boesch and Miguel Cabrera, Boston rallied in the ninth to complete the two-game sweep of the Tigers.
Jonathan Papelbon (2-0) got the win after pitching a scoreless, but hectic ninth, then the Red Sox came through against Al Alburquerque (0-1) in the bottom half.
J.D. Drew and David Ortiz each homered for Boston and Josh Beckett pitched six solid innings. He was pulled before the seventh with tightness in his neck as the Red Sox took no chances on the cool, misty night.
The Red Sox next host the Chicago Cubs when interleague play begins Friday in the first meeting between the two teams at Fenway since the 1918 World Series.
Justin Verlander went eight innings, striking out nine and holding the Red Sox to six hits and no walks.
Kevin Youkilis walked leading off the ninth and the Red Sox brought in pinch-runner Jose Iglesias, who went to third when Ortiz hit a single to right through the Tigers' infield shift. Detroit walked Drew to load the bases with nobody out and Jed Lowrie came through with a bloop to shallow left. But Andy Dirks threw home in time to force the first out.
Darnell McDonald replaced Ortiz as a pinch-runner at third and had an easy trot home when Crawford lined a ball to center field.
Papelbon got himself in trouble in the ninth, allowing consecutive singles to Brandon Inge and Austin Jackson, then walked Scott Sizemore to load the bases with one out. Papelbon struck out Boesch on three pitches, then got Cabrera swinging to keep it tied.
Beckett scattered five hits over six innings and allowed just one run, but Boston's bullpen couldn't hold a 3-1 lead.
Boesch led off the eighth with a homer to right off Daniel Bard. Cabrera followed with a drive over the Green Monster to tie it at 3-all.
Drew drove a 1-0 pitch to the seats in deep right field. Ortiz's shot through the fog in the seventh carried over the Tigers' bullpen and put the Sox up 3-1.
Beckett was pulled after only throwing 83 pitches. The team announced later that he had tightness in his neck and on the cool, wet night the Red Sox weren't about to risk losing another starting pitcher. Boston put both John Lackey and Daisuke Matsuzaka on the disabled list already this week with right elbow strains.
Beckett's only inning of trouble was the second, when he walked Cabrera to start it. Victor Martinez followed with a single to right, then after a fly out to short left, Andy Dirks drove in Cabrera with a single to put the Tigers up 1-0. The Tigers had the bases loaded with one out, but Beckett stopped the damage by getting Inge and Jackson to fly out.
Drew tied it with a sacrifice fly in the second.
Notes
Verlander struck out Boston's top three batters after allowing a leadoff single to Jason Varitek in the third. … A steady rain that had been falling in Boston let up about half an hour before gametime. … Both teams entered the game with records of 22-20. … Dirks' RBI single in the second ended Beckett's career-long scoreless innings streak at 19. … The manual scoreboard in left field had "Go Bruins" spelled out before the game, which was scheduled to start an hour before the Bruins visited the Tampa Bay Lightning in Game 3 of the NHL Eastern Conference final. … Tigers' 3B Inge turned 34 Thursday.