ESPN

CHICAGO -- The Boston Red Sox are aware of how little wiggle room there is in the competitive AL East, especially as they try to stay ahead of the Yankees for first place

"We've been playing good ball. We just have to keep it rolling. We don't have that big of a lead in the division, so we have to play good baseball," Dustin Pedroia said Sunday after the Red Sox wrapped up one of the best months of July in team history by beating the Chicago White Sox 5-3.

The Red Sox (66-40) finished July 20-6, a .769 winning percentage that beats their previous franchise record for the month -- .741 (20-7) set in 1993.

Pedroia, whose 25-game hitting streak was snapped in Friday night's opener won by the White Sox, had a two-run, go-ahead single in the seventh Sunday. And the Red Sox bullpen was stellar with 3 1/3 innings of one-hit relief.

"I'm excited to hit with guys on base, I was just trying to drive the ball to the outfield to get one run, so I was lucky we got two," Pedroia said after the Red Sox won 2 of 3 at U.S. Cellular Field.

Jason Varitek had a two-run homer and the relief trio of Alfredo Aceves (7-1), Daniel Bard and Jonathan Papelbon shut the White Sox out after they'd taken a 3-2 lead in the fourth.

"Aceves comes in like he's been doing, Bard came in and got four outs on not a lot of pitches and Pap came in and sewed it up. The extra run was nice to have," Boston manager Terry Francona said.

Adrian Gonzalez provided that with a ninth-inning double.

Boston, which added utility infielder Mike Aviles in a trade from Kansas City on Saturday, bolstered its starting staff by acquiring lefty Erik Bedard from the Mariners in a three-team deal Sunday. The Red Sox's rotation has been missing injured Clay Buchholz.

"Oh, right on. Awesome. He's got great stuff," Pedroia said of Bedard, who once pitched for the Orioles.

"We've had some injuries on our pitching staff, so we need a guy to come in here and help. Hopefully he does a great job for us. We're excited to have him. It's going to be a fun rest of the season."

White Sox star Paul Konerko left the game with a bruised calf after being hit with a pitch by Boston starter Andrew Miller in the bottom of the fourth inning. Konerko initially stayed in the game and took his base, but left after the inning ended. X-rays were negative.

With the Yankees coming to town for four games, the White Sox can ill afford to lose Konerko (.305, 25 HRs, 76 RBIs) for an extended stretch. They trail Detroit by four games in the AL Central.

"I don't expect him to be in the lineup to be honest with you. When PK took himself out of the game, it's not a concern but I know that guy was hurt," Chicago manager Ozzie Guillen said.

"When I went to the plate, I've managed him for a little while, I knew this guy can tolerate some pain and tough it out. When I got back to the dugout, I told JP (Juan Pierre) to get loose because I don't think he's going to make it."

Pierre went into the game in left field and Brent Lillibridge switched from left to first.

Chicago starter Mark Buehrle pitched six innings, giving up five hits and two runs, both coming on Varitek's seventh homer in the second. The lefty departed with a with a 3-2 lead. But the White Sox couldn't add on and had 12 runners left on base.

After Buehrle left, the Red Sox threatened in the seventh against reliever Jesse Crain (5-3) as Marco Scutaro singled, Jacoby Ellsbury got an infield single off the mound before backup catcher Tyler Flowers' passed ball allowed both runners to move up.

Pedroia then hit a two-run single to center to put the Red Sox ahead and finish Crain. Chris Sale struck out David Ortiz with runners at second and third to end the inning.

Bard pitched 1 1/3 innings of scoreless relief and Papelbon struck out the side in the ninth for his 24th save in 25 chances.

Alexei Ramirez's RBI single, Chicago's third hit of the inning, gave the White Sox a 3-2 lead in the fourth. Miller then hit Konerko in the left calf with a pitch to load the bases. Konerko stayed down for a couple of seconds and then was able to walk it off and stay in the game. And the White Sox couldn't keep their rally going.

"You get to the point when you might snap. We've got two months, a month and half, hopefully our offense will pick it up from now on and make it easier for the pitching staff," Guillen said. "And for me."

Varitek hit a two-out, two-run homer in the second to give Miller a quick lead.

But Chicago got one back in the second on Brent Morel's two-out RBI double over center fielder Ellsbury's head and another in the third when Carlos Quentin, Adam Dunn and Alex Rios hit two-out consecutive singles.

Miller gave up 10 hits and three runs in his 5 2/3 innings with one walk and a season-high eight strikeouts.

Game notes

The White Sox honored former slugger Frank Thomas by unveiling a statue of the two-time MVP on the outfield concourse. ... Bard has not allowed a run in his past 26 1/3 innings. ... The White Sox inserted DH Dunn into the lineup at first in the ninth.