Curtis Granderson led off the fifth with a home run and Marcus Thames added a grand slam in the inning, lifting the Detroit Tigers to a 9-2 victory against the Boston Red Sox on Friday night.

Detroit, which is averaging about six runs a game, won the series opener against the Red Sox, who are 53-32.

The rookie Andrew Miller (4-2) gave up one run and three hits in seven innings. He matched a season high with six strikeouts and set a career mark with four walks in his 109-pitch outing.

Julián Tavárez (5-7) allowed a season-high eight runs and matched his season high by giving up 10 hits in four and two-thirds innings.

The Tigers averaged more than 10 runs in Miller’s first five starts this season, and gave him a lot more support in his sixth.

“They’re averaging a lot of runs for everybody,” Miller said of his teammates. “It’s pretty unbelievable the way the offense is right now.”

After Tavárez held Detroit scoreless for three innings, the Tigers went ahead, 4-1, in the fourth.

Gary Sheffield led off the inning with a single, advanced on a throwing error and scored on Magglio Ordóñez’s single. Thames hit a sacrifice fly to put the Tigers ahead, and Brandon Inge’s run-scoring double gave them a 3-1 lead.

Granderson hit the first pitch of the fifth over the right-field fence for his 12th home run, giving Detroit a three-run lead. Thames’s third career grand slam, and ninth homer of the season, made the score 8-1. When Thames ran to left field to start the next inning, he was greeted with a standing ovation.

Boston had a tough time against Miller, a hard-throwing left-hander, who responded well as he faced a two-on, one-out jam in the seventh.

Tigers Manager Jim Leyland walked to the mound and the crowd rose to cheer for Miller, anticipating the end of his outing. The crowd roared when Leyland went back to the dugout without making a change. Miller’s next pitch was a 94-mile-an-hour strike to Jeff Bailey. He got out of the inning with a groundout and a liner.

Pinch-hitter Ryan Raburn, activated in place of the suspended Neifi Pérez, had an R.B.I. single in the eighth to make the score 9-1.