Sale (16-6) scattered five hits and struck out six over six innings, winning his eighth straight decision at U.S. Cellular Field and helping Chicago end a six-game skid against Kansas City. He allowed six baserunners in the first three innings before settling down to retire the last 10 batters he faced.
Addison Reed finished up, extending his White Sox rookie record with his 26th save. He allowed a two-out double to Mike Moustakas on a muffed play by left fielder Jordan Danks. Brayan Pena and Johnny Giavotella stroked RBI singles, and pinch-runner Jarrod Dyson stole second, but Lorenzo Cain struck out to end the game.
Viciedo hit a solo homer in the first for the game's first run. Flowers connected with a two-run shot in the fourth and Konerko had a solo blast in the sixth. All three homers came off Bruce Chen (10-12), who had won his last four starts in Chicago.
Chicago also hit three homers in Friday's 7-5 loss and has gone deep 28 times in its last 14 home games. Chen has allowed seven homers over his last two starts and 31 on the season, two shy of his career high.
The Royals have dominated the season series against the first-place White Sox, winning nine of 14 against Chicago even after Saturday's loss. The six straight wins against Chicago matched
Chicago had lost eight of 11 overall entering the game but still held a one-game lead over Detroit in the AL Central. The White Sox have had at least a share of the division lead since July 24.
Sale improved to 9-2 with a 1.72 ERA in 12 starts on his home field.
Chen struck out Alexei Ramirez looking in the first inning for his 1,000th career strikeout, but Viciedo made sure the celebration was short-lived by poking the next pitch into the right-field bullpen for his 20th homer, putting the White Sox up 1-0.
Billy Butler's two-out single to right tied the game in the third when Cain was ruled safe on a close play at the plate. White Sox manager Robin Ventura argued the play and he returned to the bench, but home plate umpire Mark Carlson ejected coach Mark Parent, who was yelling from the dugout.
Cain again tried to score in the eighth behind Giavotella on Alcides Escobar's RBI double, but he was gunned down by Ray Olmedo's relay throw at the plate.
Flowers, who walked twice, is hitting .356 with five homers and 10 RBIs in his last 11 games after hitting .182 with two homers in his first 33.
Konerko hit his 22nd homer in the sixth, his first round-tripper since Aug. 21.
NOTES: OF Adam Dunn missed his third straight game because of a strained right oblique. Dunn originally suffered the injury at Baltimore on Aug. 30, then re-aggravated it on Wednesday. Ventura said Dunn will have to pass a series of tests by the team's training staff before returning to action. ... 3B Kevin Youkilis missed his second straight game after returning home to be with his wife, who gave birth to a boy on Friday. Ventura said Youkilis may return to the team on Sunday. ... The White Sox are the only team in the majors with five players who have hit at least 20 homers, with Viciedo joining A.J. Pierzynski, Dunn, Alex Rios and Konerko ... Salvador Perez extended his career-best hitting streak to 13 games with a single off Sale in the second.