Along with Graffanino, who went 3-5 with two runs and three RBIs, the White Sox were led by two other bench players in Aaron Rowand and Paul Konerko, who went a combined 6-9. Konerko is now batting .197 and is 6 for his last 14.
One day after being selected to the all-star team, Magglio Ordonez drove in three runs, all on a three-run homer in the first off Indians' starter Billy Traber. The White Sox scored their final run in the first on a sacrifice fly by Joe Crede.
The inning was started with a Graffanino double and a Rowand bunt-single. Frank Thomas, 0-5 in the game, struck out before the homer by Ordonez. Carlos Lee walked, advanced to third on a Konerko single, and scored on Crede's fly out.
Garland, who heading into the day had given up four or more earned runs just once in his previous six starts, followed that path through the first four innings, giving up one run. But then four hits and one walk in the fifth brought in three more runs, tying the game, 4-4.
Dave Sanders relieved Garland, throwing 1 1/3 scoreless innings. That was followed by two scoreless innings from Damaso Marte, who picked up the win, and a scoreless ninth by Tom Gordon, earning his third save of the season and 101st of his career.
In the eighth, Konerko led off with a single and was pinch-ran for by Willie Harris. Pinch-hitter Carl Everett was intentionally walked, and after a double-steal by Everett and Harris and strikeout by Miguel Olivo, Graffanino knocked out his fifth homer, putting the Sox on top 7-4.
The Sox finished the break with a 45-49 record and seven games behind the first place Kansas City Royals. The second-half will start up on Thursday with a four-game series against the Tigers. Bartolo Colon is scheduled to start.