Both of Konerko's RBIs came in the first with a single, putting the Sox on top 2-0 over A's starter John Halama. The single came with the bases loaded and scored Frank Thomas and Ordonez, who each singled before Carlos Lee walked.
After a quick 13-pitch first, Garland gave up three runs in the A's second. The first two came from a Miguel Tejada two-run homer, with the second coming on a sacrifice fly by Scott Hatteberg. Garland walked three batters in the inning and Jose Valentin committed his seventh error of the season, leading to one unearned run.
Ordonez hit his sixth homer of the season in the third to put the Sox up 4-3, but the lead was short-lived as former Sox' catcher Mark Johnson doubled in the fourth, scoring Eric Byrnes and tying the game up at 4-4.
The Sox chased Halama in the fourth. Olivo reached first on an error by Hatteberg at first, Graffanino bunted for a single and Valentin advanced both runners with a sacrifice bunt. Thomas then hit a hard grounder to third, off the glove of third baseman Eric Chavez, for an infield single.
Jeremy Fikac replaced Halama, giving up a single to Ordonez to load the bases and a RBI-groundout to Lee, putting the Sox up 6-4.
Homers in the fifth by Chavez for the A's and Olivo for the Sox was the final scoring for both teams.
Kelly Wunsch started the sixth inning in place of Garland, but recorded just one out and allowed two baserunners before being pulled for Tom Gordon. Gordon ended the inning and followed up with scoreless seventh and eighth innings.
Billy Koch started the ninth inning with a walk, two rather long fly balls and a single before being replaced by Damaso Marte. Marte recorded the final out to pick up his second save.
The Sox will begin a three-game set on Friday against the Mariners at 7:05 p.m. CT. Esteban Loaiza is scheduled to pitch against righty Ryan Franklin.