Konerko's tiebreaking three-run homer was his 400th for the White Sox and Chicago routed the Cleveland Indians 12-6 on Sunday to complete a three-game sweep.
The White Sox have won five straight for the first time this season and nine of 10 overall.
Konerko, who extended his hitting streak to 13 games, also came out for a curtain call after fans chanted "Paul-ie!" Paul-ie!" following No. 400.
"It's probably the thing I'm proud of most, more than any numbers," he said. "I'm proud of that one fact of just being here as long as I have."
Drafted by the Dodgers in 1994, Konerko played in 55 games for Los Angeles and 26 for Cincinnati before coming to Chicago in a trade after the 1998 season.
The 36-year-old first baseman hit 31 homers last season and 39 the year before that.
"He's figured something out," Gordon Beckham said of Konerko. "The last three years it just seems like he's been unbelievable. It's fun to run out on the field every day with him, that's for sure."
Chicago has homered in 13 consecutive games for the first time since 2006, and scored nine or more runs in four consecutive games. The White Sox haven't accomplished that feat since June 27-30, 1938, the White Sox said, citing the Elias Sports Bureau in statistics distributed by the team.
In the fourth inning, Konerko battled back from an 0-2 count against Ubaldo Jimenez in the fourth inning and deposited the eighth pitch of the at-bat into the left-center field seats to give Chicago a 7-4 lead.
Konerko finished with two hits and four RBIs, and raised his average to a majors-best .399.
"Paul Konerko is just a professional hitter and he has been for years," Indians manager Manny Acta said. "There's only so much you can do. He's a good one."
Johnny Damon hit a three-run homer for the Indians, his first of the season, and Jimenez (5-4) struggled over four-plus innings. He gave up seven runs and seven hits, walked four and struck out three.
Gavin Floyd (4-5) wasn't much better. He allowed five runs on 10 hits over five-plus innings. He also hit three batters with pitches.
The White Sox beat the Indians 14-7 on Saturday and 9-3 on Friday. They have scored 93 runs in their last 13 games.
Jimenez (5-4) gave up seven runs in four-plus innings. He walked four and struck out three.
"Ubaldo didn't throw enough strikes and had a tough time putting hitters away," Acta said. "He gave up two-strike hits that really hurt him and just couldn't locate his pitches."
The Cleveland right-hander is 1-3 with a 6.21 ERA in six career starts against the White Sox.
Floyd He has given up 21 runs over his last three starts, but the offense was able to bail him out this time.
Chicago jumped out to an early lead with three runs in the bottom of the first. Konerko drove in the first run on a fielder's choice after Jimenez loaded the bases with nobody out. Alex Rios and Alexei Ramirez followed with RBI singles.
Cleveland tied the game quickly in the second on Damon's homer. Things could have been much worse for Floyd, who struck out three in a row after allowing the first five Indians to reach.
Ramirez put the White Sox back in front with a two-out RBI single in the third, but Michael Brantley's run-scoring single tied it again.
Floyd again dodged trouble by turning a one-out comebacker into an inning-ending double play with the bases loaded.
The White Sox tacked on three more in the fifth on back-to-back triples by Orlando Hudson and Alejandro De Aza.
Dayan Viciedo drove in two with a bases loaded single in the ninth.
Cleveland catcher Lou Marson was hit in the face by a pitch in the fourth inning and left the game in the fifth with what the team said was a bruise. Cleveland placed No. 1 catcher Carlos Santana on the 7-day disabled list Saturday after diagnosing a concussion.
Juan Diaz led off the third with a single for the Indians, his first big league hit. He also singled and scored in the sixth.
NOTES: White Sox 3B Brent Morel (back) took batting practice Sunday and is hoping to begin a rehab assignment on Wednesday with Triple-A Charlotte. . LHP John Danks (shoulder) played soft toss on Sunday and said his arm feels "better than it did a few days ago," noting that he still feels some discomfort in the back of his arm. . Indians SS Asdrubal Cabrera (tight left hamstring) will run and take batting practice on Monday. He hasn't played since leaving Friday night's game in the seventh inning. . Chris Sale (5-2, 2.50 ERA) pitches the series opener for the White Sox in Tampa Bay on Monday. Josh Tomlin (1-2, 4.67) will go for Cleveland against Kansas City.
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