The game-winning run came in the 10th inning by way of a double down the left field line by Frank Thomas, scoring Tony Graffanino -- who singled -- all the way from first base.
The wasn't the only damage done by Thomas, who went 3-4, hitting his team-leading 11th home run in the sixth off Diamondbacks starter Elmer Dessens. Brian Daubach hit his first homer of the year two batters later, also a solo shot, giving the Sox the then 2-1 lead.
Thomas now has an eight-game hitting streak, where he is 12-29 with nine RBIs, five doubles and two home runs.
Danny Wright and co. threw what may have been their best game of the season, allowing just two runs, both via solo homers off the bats Tony Womack and Junior Spivey in the fifth and sixth innings.
Take them away and Wright gave up just one hit over six innings. Sox pitching allowed just five baserunners total. Wright struck out four and threw 80 pitches.
Marte and Koch, in order, each threw two scoreless innings, with Koch picking up the win.
Jose Valentin and Graffanino each had two hits on offense, making the top third of the Sox batting order 7-13 in the game. The rest of the offense went 4-25.
The Sox will now head to Los Angeles to start a three-game series against the Dodgers on Friday at 9:10 p.m. CT, with Mark Buehrle going up against Kazuhisa Ishii. The game will be televised on Fox Sports Net Chicago.