CHICAGO -- Headed to the plate with the bases loaded in a tie game, Ryan Raburn would have been happy with a base hit.
Instead, he drove the first pitch he saw from Jake Peavy into the left-field bullpen to stun the crowd at U.S. Cellular Field.
"That's what we're working hardest on is getting runners in when we get the opportunities," Raburn said. "Fortunately for me, it went over the fence ... but I definitely would have taken a single."
Raburn was mired in a 6-for-52 slump before his third career grand slam. The 30-year-old has a hit in each of his past five games and is beginning to see things turn around.
"I'm getting close," he said. "Consistency is still not there but I feel a lot better and as long as I can keep getting that one hit, hopefully it will turn into two or three hits."
The Tigers captured the last two in the weekend series at Chicago to move within 2½ games of AL Central-leading Cleveland, which lost 2-0 to Texas on Sunday. They have won 11 of their last 12 games against the White Sox overall.
Brad Penny (5-4) rebounded from a shaky first inning to pick up the victory. He allowed three runs and eight hits, struck out five and walked two in five innings.
"(The White Sox) had a lot of foul balls to get his pitch count up," Tigers manager Jim Leyland said. "He had good stuff. It wasn't his best, but he battled through it and picked up a win."
Peavy left with a strained right groin after allowing six runs in the fourth inning, including Raburn's slam. Peavy's 2010 season ended when he injured his right shoulder on July 6.
Peavy said the injury dates to his previous start in Boston on May 30.
"I didn't think too much of it until after the second inning (Sunday)," Peavy said. "It was grabbing bad enough for me to come out and do a wrap job, and took a couple of Tylenols."
Chicago pushed across two runs in the first and Peavy (2-1) retired the first nine batters before running into trouble in the fourth.
Austin Jackson reached on a leadoff single and Don Kelly followed with a bouncer to first baseman Paul Konerko, who threw to second for one, but shortstop Alexei Ramirez's throw back to Konerko pulled him off the base and Kelly was safe. Peavy then walked Brennan Boesch and threw a wild pitch, putting runners on second and third.
After Cabrera drew a walk in a 13-pitch at-bat, Victor Martinez hit a sacrifice fly and Andy Dirks tied it with an RBI double. Another walk, this one to Alex Avila, loaded the bases for Raburn, whose last grand slam came on May 15, 2009.
Penny was backed by four scoreless innings from the Detroit bullpen. Adam Dunn's leadoff single in the sixth and Ramirez's two-out infield single in the ninth were the only hits for Chicago after Penny departed. Closer Jose Valverde got Konerko to line out with runners on first and second to end the game.
Peavy allowed six runs, three hits and walked three in his fifth start since he rejoined the team on May 11 after recovering from shoulder surgery. The 2007 NL Cy Young Award winner threw 75 pitches and will be re-evaluated on Monday.
Since being traded to the White Sox on July 31, 2009, Peavy is 12-7 in 27 starts. He was bothered by ankle problems in 2009 and went 3-0 in three late starts for the White Sox. He made 17 starts last year and was 7-6 before his season was cut short by the shoulder injury.
Cabrera hit his 13th homer off Will Ohman in the sixth. He also had a tiebreaking two-run homer in the ninth inning of Saturday's 4-2 win.
Konerko was back in the lineup after undergoing a minor procedure to dislodge a loose fragment in his left wrist on Friday. He hit an RBI double in Chicago's two-run first.
White Sox second baseman Gordon Beckham homered for the second straight day. His solo drive in the fourth was his sixth of the season.
Dunn was 1 for 4 with three strikeouts. He struck out in the eighth, igniting boos from the crowd.
White Sox manager Ozzie Guillen gave CF Alex Rios the day off. He is in a 6-for-40 slump covering his last 10 games. Guillen said he might also rest Rios on Monday against the Mariners. ... The White Sox activated INF Mark Teahen from the 15-day DL and designated RHP Jeff Marquez for assignment.