SARASOTA, Fla. -- Jon Lester allowed just one run in his first Grapefruit League start, and the Red Sox took advantage of Chris Davis' second-inning error for a pair of runs and never looked back in a 6-1 win over the Orioles on Sunday afternoon.

Lester, who is 14-0 in 18 regular-season starts vs. the Orioles, allowed one hit and notched two strikeouts, but he also issued four walks. The southpaw retired seven of the last eight batters he faced to end his first Grapefruit League start on a high note.

"About halfway through the second, I finally got into a little bit of a rhythm," said Lester. "We had kind of a hard time figuring out where the plate was. I was just missing on a lot of pitches, but I felt good and ended up limiting the damage. That was the main thing."

Journeyman Dana Eveland struggled for the Orioles, allowing three runs (one earned) and only went two innings instead of the originally scheduled three. Eveland, who consistently fell behind most of the Red Sox's lineup, didn't do much to help his case in the team's starter/bullpen competition, and he was followed by a perfect inning from lefty Zach Phillips.

Red Sox second baseman Dustin Pedroia went 2-for-3 with a pair of RBIs, while Cody Ross had a pair of hits and two runs scored.

O's right-hander Chris Tillman allowed just one hit over three scoreless innings, while Luis Ayala allowed a run in the seventh after issuing a pair of back-to-back walks.

Adam Jones put Baltimore on the scoreboard in the first inning, when he laced an RBI single to right field, but he was thrown out while trying to stretch it into a double.

Non-roster invitee Aaron Cook, who is trying to win a job in Boston's rotation, pitched two scoreless innings.

"It felt really good," said Cook, who walked two batters in his first inning of work. "The first inning, I was a little amped up. I felt like a little kid. I was able to make some pitches and get out of the inning. [I] got a lot of ground ball [outs], and that's what I need to do."

Up next for the Red Sox: New closer Andrew Bailey will make his Grapefruit League debut out of the bullpen Monday in a 1:35 p.m. ET airing live on MLB.TV against the Marlins. Veteran right-hander Josh Beckett will make his third start, and setup man Mark Melancon is also scheduled to pitch. Adrian Gonzalez and Kevin Youkilis will be back in the lineup after getting Sunday off.