BALTIMORE (AP) — Ryan Dempster pitched well enough to win. Boston’s offense didn’t do enough to make it happen.

The Red Sox wasted a solid start by Dempster, managing only three hits off Chris Tillman and three Baltimore relievers in a 2-0 loss Friday night.

Tillman took a two-hitter into the seventh inning and Chris Davis hit his major league-leading 22nd home run for the Orioles, who moved within 1½ games of first-place Boston in the AL East.

Jose Iglesias contributed two hits for the Red Sox and Shane Victorino had one. That was pretty much it for the Boston attack.

“We weren’t able to combine walks and hits in the same inning as we have for the vast majority of the season,” manager John Farrell said. “The rare occasion where we’re left with zero on the board.”

Boston, which leads the majors in runs, absorbed its fourth shutout.

Making his first career appearance at Camden Yards, the 36-year-old Dempster (4-7) gave up two runs and five hits in 7 2-3 innings. Unfortunately for the right-hander, the Red Sox got only one hit after the fourth and now have gone 15 straight innings without scoring a run.

“The guy just pitched his tail off over there,” Dempster said. “Sometimes you just get outpitched. There is really nothing you can do about it. We don’t get shut out very often. It’s kind of a rarity. … I felt good about my outing, for sure. I felt like I pitched well. The other guy just pitched better than me.”

Boston catcher David Ross said of Dempster: “Ryan did a great job, threw a great game. That was a huge, huge performance. Those last innings, I think, were his best innings. The slider was really sharp, fastball was sinking.”

Baltimore got only one hit after the third inning, but by then it was 2-0.

Tillman (7-2) allowed three hits and four walks in six-plus innings. The right-hander permitted only one runner to get past second base in winning his third straight start.

After Iglesias chased Tillman with a leadoff double in the seventh, Darren O’Day got three successive outs. Tommy Hunter worked a perfect eighth and Jim Johnson completed the three-hitter to earn his 24th save.

Boston has lost two in a row for the first time since May 28-29 against Philadelphia, and its streak of winning four consecutive series is over. The Red Sox are 1-4 against the Orioles this season and have won only four of the last 17 games between the clubs.

Davis led off the second inning with an opposite-field drive into the left-field seats, his sixth homer in the last eight games against the Red Sox.

“I think Chris knows he doesn’t have to get into pull mode to be effective,” Showalter said. “That’s been good for him.”

Baltimore made it 2-0 in the third. Nate McLouth walked, took second on a single, advanced on a fly ball and scored when Adam Jones reached on a two-out dribbler down the third base line.

Tillman issued a walk in each of the first four innings but kept the Red Sox at bay. After Boston got runners on the corners with one out in the fourth, Will Middlebrooks hit a short fly to right and David Ross struck out.

“We did get a couple of guys on base over the course of the game, but it was a night where we couldn’t bunch anything together,” Farrell said. “He did issue the four walks to give us a couple of opportunities. Still, when you take (Iglesias) out of the mix, where he got two out of three hits in that ballgame, Tillman did a good job of keeping us in check.”

NOTES: Baltimore’s Manny Machado hit two doubles to increase his majors-leading total to 30. He also extended his hitting streak to 12 games, a new career high. … The Red Sox recalled RHP Rubby De La Rosa from Triple-A Pawtucket and optioned RHP Alex Wilson to the same club. … The Orioles recalled RHP Jake Arrieta to fill out their weary bullpen. … After being designated for assignment Monday, Boston INF Pedro Ciriaco was traded to San Diego for a player to be named or cash. … John Lackey will start for Boston on Saturday against Baltimore and Freddy Garcia. Lackey is 11-4 lifetime against the Orioles and Garcia is 10-4 vs. Boston. … J.J. Hardy went hitless against Dempster and is 2 for 30 lifetime against the right-hander. … Iglesias has hit in 15 straight games in which he has a plate appearance. … The Orioles reinstated LHP Tsuyoshi Wada (elbow) from the 60-day disabled list and optioned him to Norfolk. … McLouth stole his 23rd base, tying a career high.