A.J. Pierzynski went 3-for-4 with two RBI and two runs scored for the White Sox, who have won a season-high seven in a row and 11 of 12 overall. Omar Vizquel knocked in two runs for the victors.
John Danks (7-5) was solid in seven innings, allowing three runs on six hits to pick up his third straight win. The left-hander also struck out three and walked one.
"You don't want to be the guy to snap the streak," Danks said. "You don't want to be the weak link. We are all feeding off each other, and we're all throwing the ball well and hopefully we'll continue to do that the rest of the year."
Tommy Hanson (7-4) had his worst outing of the season, giving up nine runs on 13 hits to suffer his first loss since May 15 versus Arizona. The right-hander was 4-0 with a splendid 2.03 earned-run average over his previous five starts coming into Tuesday.
Prado led off the first inning with a homer to left to give the Braves an early lead. Conrad hit a two-run double during Atlanta's next at-bat to give the visitors a 3-0 margin.
The White Sox took control from there, starting with a five-run second. Paul Konerko and Quentin got things started with consecutive singles. Both runners advanced a base on a groundout and crossed the plate on Pierzynski's single. Alexei Ramirez singled and Juan Pierre was hit by a pitch to load the bases with two outs. Vizquel followed with a two-run base hit to right. Alex Rios capped the scoring in the frame with an RBI infield single for a 5-3 lead.
Ramirez's run-scoring single in the third made it a three-run game. Quentin smacked a three-run homer during Chicago's next at-bat to make it a 9-3 contest.
Danks retired 11 straight batters before giving up a one-out single to Chipper Jones in the sixth. Danks, though, retired the next two batters to get out of the inning unscathed.
The Braves scored a run in the eighth to cut the gap to 9-4. Tony Pena gave up a leadoff triple to Prado, who crossed the plate on Heyward's groundout.
In the ninth, McCann homered and Conrad hit an RBI double to account for the final margin.
"He settled in and threw really well against us. Tip your cap to him," Conrad said of Danks. "We just couldn't put enough across the board tonight."
These teams last opposed one another back in 2004, with the White Sox taking two of three games from the Braves in Chicago...The Braves activated pitcher Takashi Saito from the 15-day disabled list and optioned pitcher Craig Kimbrel to Triple-A Gwinnett...The White Sox agreed to terms with pitcher Chris Sale on Tuesday...Chicago started a six-game homestand on Tuesday...Bobby Jenks recorded the final out in the ninth to pick up his 15th save of the year...The White Sox last won seven straight games from June 27-July 3, 2009...Prado has 34 multi-hit games this season.