"We've got nothing to lose," Konerko said. "There's no pressure on us and we shouldn't play with any pressure ... It's really the Twins' to lose."
Konerko hit a pair of two-run homers and an RBI single in Chicago's come-from-behind 12-6 win over the Kansas City Royals on Sunday.
The win helped the White Sox keep pace in the Central, six game back of the Twins. The teams play three games in Chicago beginning Tuesday.
"We know it's uphill," Konerko said of the six-game deficit. "You can't sweep unless you win the first one. [But] if we can win two out of three at least and put a little more heat on them, there's still some games left after that. But a sweep would be nice."
Chicago Pinch-hitter Andruw Jones had the other big hit, a grand slam in the sixth inning.
"The way they were swinging [early] the question was whether we would hold them," Konerko said. "Starting last night they were swinging the bats great ... it had that feel it was going to be a slugfest."
Kansas City led 6-0 after just one-half inning, but Chicago chipped away with two runs apiece in the first, third and fourth innings before chasing Royals starter Sean O'Sullivan, who gave up five runs.
"You've got a young kid on the mound and a young offense," Royals manager Ned Yost said. "It never turns out the way you want it to because the pitcher thinks he has room to make mistakes, the offense thinks they've scored some runs."
Reliever Sergio Santos (2-0) pitched 1 1/3 scoreless innings for the win, striking out three. Philip Humber (1-1) tossed 2 1/3 innings and gave up four runs and five hits.
The Royals sent nine batters to the plate in the first, scoring six runs on starting pitcher Lucas Harrell thanks pair of three-ru home runs each from Billy Butler and Brayan Pena.
Butler's drive was his 12th of the season while Pena's was his first since Sept. 26, 2009, against Minnesota.
Konerko connected for his 35th homer of the season in the bottom half. Konerko hit his second two-run shot in the third, this time sending a 1-2 pitch on a towering fly to left field. He now has 27 career multihomer games, the last coming on June 2 against Texas.
Chicago tied the game with a pair of fourth-inning runs. Juan Pierre had a sacrifice fly while Alexei Ramirez scored from third on a passed ball with Konerko at the plate.
Harrell settled down after the first and eventually pitched 3 1/3 innings. He gave up six earned runs on nine hits, walked three and struck out one.
In the decisive sixth, the White Sox had runners on first and third when Konerko delivered a single that brought home Omar Vizquel. Humber then hit Manny Ramiez with a pitch to load the bases.
Dusty Hughes entered in relief and walked A.J. Pierzynski to score Alex Rios for an 8-6 lead.
Jones, pinch-hitting for Mark Teahen, hit his fifth career slam on a 1-2 pitch to left-center.
Royals second baseman Chris Getz left the game with a mild concussion after being hit in the head on a throw from Pierzynski, the catcher, while running to second in the fifth inning. The Royals said he'd be evaluated on Monday.Notes
Konerko's two home runs gave him 362 for his career. He moved ahead of Joe DiMaggio for 69th on the all-time list. ... Pierre picked up the 514th stolen base of his career in the bottom of the first inning.