CHICAGO -- Staked to a four-run lead in the first inning, there was no way Jake Peavy was letting this one slip away.
Rios hit a grand slam in the first inning and a two-run shot in the sixth to help extend Chicago's lead in the AL Central to 1 1/2 games over Detroit, which plays Wednesday night.
"Every night you go out it's a huge challenge in front of you," Peavy said. "The bottom line is to grind and flat-out want it more."
The Twins erupted for 18 runs against Chicago pitching Tuesday, but Peavy (10-10) silenced Minnesota's bats a day later, allowing one run on six hits to win for the first time since Aug. 1.
"(Peavy is) the kind of guy you want after a game like that," White Sox manager Robin Ventura said. "He came out and battled, did great, and Rios hits a couple homers."
"Things look all right again."
Rios gave Peavy all the support he would need with his first-inning slam. Following Dewayne Wise's leadoff single and walks to Kevin Youkilis and Adam Dunn, Rios ripped a 1-1 pitch from P.J. Walters (2-3) over the left field bullpen for his second career grand slam.
Rios hit his first on Sept. 10, 2011 -- a game-winner against Cleveland.
"He's been consistent all year long," Ventura said of Rios. "It's a good day for him to come in here, especially after last night, you get waxed and come back and get something early."
The resurgent 31-year-old then hit a two-run homer in the sixth to chase Walters. It was Rios' third multihomer game this year and sixth of his career.
"I just got a few good pitches and I connected well so that's all you can hope," Rios said. "Hit the ball hard and see what happens."
The White Sox had won just one of their last 10 games against AL Central opponents.
Walters, who tossed his first career complete game at U.S. Cellular Field in May, was not as fortunate this time in his first start since June 13. He made two big mistakes to Rios, but Walters also issued three walks -- all of which came around to score.
"I wasn't missing by a whole lot, but enough to be balls," Walters said. "That's the big part of the game -- not so much the homers, but the three walks. I don't walk those three guys ... maybe it plays it out a little different."
Walters was charged with six runs over five-plus innings as the Twins lost for the 11th time in 15 games against Chicago this season.
"Take Rios out of the game and we're still playing, but you can't take him out because he took us out," Twins manager Ron Gardenhire quipped.
An offense that tormented White Sox pitching a night earlier was virtually nonexistent Wednesday. The Twins had multiple runners on in three of the first six innings, but managed to scratch just one run off Peavy on a sacrifice fly by Eduardo Escobar in the third.
Twins OF Josh Willingham (hamstring) did not start Wednesday for the second time in three games. He flew out as pinch-hitter in the ninth to end the game. Gardenhire said he hopes Willingham can play in the field Friday in the series opener against Cleveland. ... RHP Liam Hendricks (0-7, 6.11 ERA) will take the hill to open Minnesota's homestand Friday. ... After a day off Thursday, the White Sox continue their homestand against Kansas City with LHP Francisco Liriano (5-11, 5.11) on the mound.