Jose Abreu had three hits, including a pair of RBI doubles.
Gio Gonzalez was pulled one out shy of the win. He allowed two runs and six hits in 4 2/3 innings.
"It's always frustrating," Gonzalez said. "You never want to give up the ball in a situation like that."
Matt Foster (2-0) was credited with the win after striking out four in two perfect innings.
Tyler Alexander (1-1) allowed five runs in 3 2/3 innings in his first start of the season. His previous appearance was a memorable one -- he struck out an American League record-tying nine straight hitters during a relief appearance Aug. 2 against Cincinnati.
"His breaking ball wasn't sharp. For the most part he got things up. That's a powerful lineup. Just one of those days," Detroit manager Ron Gardenhire said. "The kid's been throwing great. We've all seen it. It just didn't work out today."
Abreu opened the scoring with a run-scoring double in the first, and Jimenez's home run to right field made it 4-0. Encarnacion hit a solo shot in the fourth.
Romine's homer came in the fifth. Jimenez hit an RBI single in the sixth, and the White Sox added two more runs in the seventh.
Harold Castro hit an RBI single as part of Detroit's two-run ninth.
Gonzalez was taken out with two outs in the fifth, a man on first and Miguel Cabrera coming up. Chicago replaced the left-hander with Jimmy Cordero, and the righty threw only one pitch, retiring Cabrera on a lineout to the shortstop.
White Sox manager Rick Renteria said he came close to leaving Gonzalez in.
"As I tell all my pitchers, when I think you're out of outs, I go get you," Renteria said. "It's best to make a move one pitch too soon than one pitch too late."
White Sox: Chicago reinstated SS Tim Anderson (strained right groin) from the injured list before the game and put INF Leury Garcia (sprained left thumb) on the IL. Anderson had a walk, a hit and two runs.
Tigers: Detroit put 1B C.J. Cron on the injured list before the game with a left knee sprain. Trainer Doug Teter said Cron has damage to a ligament and there is no timetable for his return.
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