Beckett (4-2) gave up six hits and a run in seven innings.
"I thought we had good at-bats off Beckett. I thought we battled him hard," Tigers manager Jim Leyland said. "One thing you have to do when you face a guy like Beckett, you got to hold down the other team, we didn't do that."
Verlander (1-6) gave up five runs on nine hits in six innings. He struck out five, but allowed Kevin Youkilis' two-run homer in the fifth and Jason Varitek's two-run single and Jacoby Ellsbury's sacrifice fly in the second inning.
"Obviously the big hit was Youkilis hitting the home run," Verlander said. "Looking back, it was because I was flying off a little bit, I was trying to go down and away, and it runs back in the middle of the plate. He didn't hit it great but he got decent enough wood on it to get it elevated and get it over the fence."
Youkilis has three homers in the last two games and eight in his career at spacious Comerica Park. He hasn't hit more than two at any other road park.
"Our entire staff did a poor, poor job the entire series against Youkilis," Leyland said. "Not with the thought process but executing pitches. We just gave him cookie after cookie and he just beat our brains out."
The Red Sox took three of four in the series from the Tigers and have won six of their past seven, while Detroit has lost six of seven.
"I made pitches when I needed them, and that's what it boils down to," Beckett said. "If I hadn't been able to make a couple key pitches, I would have given up a lot more runs. I had all four pitches working when I needed them, and that's big."
Red Sox manager Terry Francona said, "You don't want to take him for granted, but he had a lot of good pitches against a very dangerous lineup."
Boston left two runners on in the seventh, and left the bases loaded in the eighth but Detroit couldn't take advantage.
"We gave them a chance in those two innings but [Craig] Hansen came in and silenced them in the eighth, which helped a lot," Varitek said.
Boston RHP Curt Schilling played long toss before Thursday's game, continuing his rehabilitation from a shoulder injury. He threw 25 balls from 60 feet away. ... Boston LF Manny Ramirez, Tigers LF Gary Sheffield and C Ivan Rodriguez had regularly scheduled days off Thursday. ... Youkilis hit four home runs in the series this week. ... Verlander didn't lose his sixth game last year until Sept. 18th.