MINNEAPOLIS — The Chicago White Sox climbed out of an early hole created by starter Dylan Axelrod, only to lose another close game.

Chicago fought back after Axelrod allowed four of the first five Minnesota Twins he faced to score, but Ryan Doumit’s two-run double off Ramon Troncosco broke an eighth-inning tie and the Twins won 7-5 on Tuesday night.

Paul Konerko had a season-high four hits for the White Sox, who lost for the fifth time in their last six games and have won just five of their last 20. Eleven of those 15 losses have come by three runs or less.

“I still think there’s some good to come out of this at some point,” Konerko said. “It hasn’t been right now, it hasn’t been before now, but we still have good baseball in us. We just haven’t shown it.”

In a season featuring little to praise, at least Axelrod didn’t overtax Chicago’s bullpen.

The right-hander threw a season-high 114 pitches and allowed 10 hits with a pair of walks.

Deunte Heath was warming for Chicago before the first inning ended, but Axelrod managed to pitch through the sixth and gave up only one more run. Pitching on seven days rest after giving up six runs in his previous start, Axelrod retired 12 of 13 stretching from the second through sixth innings before allowing three straight hits for Minnesota’s fifth run.

“Obviously what I was doing wasn’t working out too good,” Axelrod said. “I decided to throw inside a little bit more, keep them honest. It worked out.”

With Ventura planning to rest Jesse Crain and Nate Jones after the duo combined for three innings Monday, the extended outing was especially important.

“(Axelrod) after that kind of calmed himself down and gets through it, gives us a chance,” Ventura said. “Guys fight back. It’s just one of those you tip your hat to them in that eighth inning.”

Troncosco (0-2) retired Trevor Plouffe to end the seventh inning with two runners on, setting up Konerko’s game-tying RBI single off Jared Burton (1-4) in the eighth. The right-hander, making just his fourth appearance of the season for the White Sox, set down the first two Twins he faced in the bottom of the frame before a walk and a single set up Doumit’s double — his third hit of the game.

Minnesota closer Glen Perkins pitched the ninth for his 17th save.

Joe Mauer hit a two-run homer in the Twins’ four-run first. Conor Gillaspie responded for the White Sox with a two-run shot of his own in the second.

Konerko’s four-hit game was his first since July 24, 2012, against Minnesota and raised his batting average 13 points to .248.

“All you can control is your approach and if you’re going about it right,” Konerko said. “I’ve been doing it right, did it right tonight, hopefully keep doing it right tomorrow.”

Twins starter Mike Pelfrey lasted six innings, ceding a season-high 10 hits and four runs.

Notes: Gillaspie is now second among AL rookies with five home runs. … Minnesota CF Aaron Hicks is running in the outfield and making progress rehabbing from a strained left hamstring. Twins manager Ron Gardenhire said Hicks — on the disabled list since June 10 — will probably have to complete a rehab assignment before returning to Minnesota. … A bus transporting the Twins Elizabethton, Tenn., rookie league affiliate was involved in a bus crash that killed a driver traveling the wrong way down a highway in Florida. … Josh Willingham was back in left field for the Twins after missing two games with a sore knee. … Coming off a start where he fanned 14, didn’t allow an earned run, but lost 2-1 at Houston, Chris Sale (5-5, 2.43 ERA) starts for Chicago on Wednesday. … The Twins will counter with Kevin Correia (5-4, 3.97 ERA), who is 1-5 since April 23.