Jimenez (3-2) gave up two runs on three hits while walking five batters. He also struck out a pair.
Zach Stewart (2-4) was tagged with the loss after giving up three runs on seven hits over five frames. He struck out four and walked a pair.
"I wasn't hitting my spots like I was last time out," Stewart said. "My breaking ball wasn't sharp and I got hit around a little bit."
Cleveland opened the scoring in the second, plating three runs to take an early lead. After Travis Hafner and Shelley Duncan struck out, Lonnie Chisenhall stroked a single to right to begin the rally and Valbuena followed with a base hit to put runners on the corners. Crowe then singled home Chisenhall for the first run of the game, and Lou Marson doubled in Valbuena and Crowe for a 3-0 advantage.
The White Sox got two runs back in the third. Alejandro De Aza manufactured the first run of the inning for Chicago when he singled to begin the frame, stole second and third and trotted home on a fielder's choice by Beckham. Juan Pierre then singled and Beckham moved to third to put runners on the corners with one out. Ramirez grounded into another fielder's choice, allowing Beckham to score to pull Chicago within one.
Cleveland threatened to expand its lead in the fourth. Valbuena ripped a single to start the inning and moved to second on a groundout by Crowe. Kosuke Fukudome was intentionally walked two batters later to give the Indians runners on first and second. Cleveland was unable to capitalize, however, as Jason Donald grounded into a force out at second to end the inning.
The White Sox answered with a threat in the home half of the inning when Jimenez struggled to find the strike zone. Things started well, as A.J. Pierzynski grounded out, but Jimenez walked Dayan Viciedo, Alex Rios and Brent Morel to load the bases with two outs. He recovered to strand the bases loaded, getting Beckham to ground out to third to end the inning.
Cleveland tacked on another run in the sixth courtesy of a solo-shot from Valbuena into the right field seats to make it a 4-2 game.
The Indians broke the game open in the eighth with three more runs to make it a 7-2 game. Chisenhall ripped a single to begin the frame, Crowe singled two batters later and Marson walked to load the bases with one out. Following a Fukudome fly out, Donald beat out an infield single which allowed Chisenhall to score. The big hit of the inning came off the bat of Santana, who cracked a two-run double into right field corner to give the Indians a commanding lead.
"The bottom of the order did it for us," Indians manager Manny Acta said. "Especially Carlos with that huge two-run double to give us a cushion. We needed it."
Chicago picked up a run in the ninth on an RBI single by Pierre to account for the final margin.
Chicago is 2-2 on its current seven-game homestand...White Sox first baseman Paul Konerko, who went 0-for-5, is one homer shy of his seventh career 30- home run season...Donald has hit safely in 13 of his last 15 games...It was Valbuena's first homer of the season.