After Matusz finished the sixth, Pedro Strop, Darren O'Day and Jim Johnson each working a scoreless frame.
“We know what we have to do,” Johnson said. “We're playing against teams in our division and obviously all these games mean a lot. They're a good team and they're totally different than what they were last year. It's going to be a dogfight all the way through. And we know that and they know that. Any time you can win a series and move on to the next city, you're happy.”
The Red Sox plated two runs off Tillman in the third to take a 2-1 lead, with both runs scoring with two outs. Dustin Pedroia hit an RBI single to right, and Mike Napoli followed with an RBI single to left that fell just in front of a sliding Nate McLouth.
The Orioles failed to score with the bases loaded and two outs in the fourth when No. 9 hitter Alexi Casilla struck out to end the inning. Orioles No. 9 hitters are 2-for-20 since Brian Roberts was injured last Thursday.
In Davis' first at-bat of the game in the second inning, he crushed an offering from Boston starter Alfredo Aceves over the wall in deep center, a solo shot that put the Orioles up 1-0.
Davis, who hit a solo homer to start the Orioles' ninth-inning rally Wednesday, has homered in 13 of his last 16 games dating back to Sept. 26. Included in that stretch are consecutive homer streaks of four and six games.
“Our guys should be proud of their effort the last two nights, and really the last three nights,” Orioles manager Buck Showalter said, “and we move on to another challenge in New York.”