MINNEAPOLIS — The White Sox, 14-24 since the All-Star break and owners of a 56-68 record after defeating the Twins 6-4 on Monday night, have nothing to fight for as they head for the finish line of a seventh consecutive losing season.

They can annoy teams like the American League Central leaders, which they did Monday using a lineup with Jon Jay batting in the cleanup spot protecting Jose Abreu, and with Matt Skole at designated hitter, where the Sox are an anemic .179/.262/.310 this season.

They are 17½ games behind the second-place Indians, so there’s no chase there, and 11½ games ahead of the Royals, so there’s no worry about finishing fourth for the sixth time in Jose Abreu’s six seasons as a Sox.

Poor Abreu. He has been the consummate good soldier for teams that haven’t had the ammo. But he’s confident it will be his last season out of contention.

Wait till next year, he said.

“I truly believe that we are going to be in a good position next year to compete for a playoff spot,” he said through an interpreter. “I know that the front office is going to make the move that will be the right move for us to move forward and to get to that final phase of this process.”

Abreu wouldn’t go so far as to say it needs to be a huge acquisition — just the right one. And he’s as confident as ever that he’ll be back with the Sox, even as his contract expires at the end of the season.

“Of course,” he said. “Like I said before, if the team doesn’t sign me, I’m going to sign myself here.”

At 32, he looks to have something to offer yet. Against Twins righty Kyle Gibson in the third inning, he launched a 442-foot homer to left-center, almost to the third deck at Target Field. It was his 27th home run and longest of the season and lifted his RBI total to 92.

“When you make that kind of connection, you don’t feel the ball hit the bat,” Abreu said. “Once you see the ball fly, you say, ‘OK, that was a good one.’ ”

Abreu’s blast gave the Sox and right-hander Ivan Nova — who downsized 10 hits allowed into 5⅓ innings of two-run ball — a 4-2 lead. Nova (9-9) has an 0.85 ERA over his last six starts, and he liked this one the most because he got by without his best stuff.

Asked what matters between now and the end of the season, Abreu had a few answers: Eloy Jimenez keeping his development on track, and Yoan Moncada — who was finishing a rehab assignment after a strained hamstring — getting back to performing like a star as the Sox wait for Class AAA Charlotte center fielder Luis “La Pantera” Robert, who belted his 28th minor-league homer Monday.

“La Pantera, keep growing, doing his job and learning, and hopefully we can get him at any point,” Abreu said. “He’s going to be a big key for us in the future. And as a team, just keep battling. Keep doing our job, keep trying to do our best every day and winning as many games as we can.”

The Twins, who had won four straight, pelted Nova with two quick runs in the first. Ryan Goins’ RBI single preceded Abreu’s homer in a four-run third, and Yolmer Sanchez squeeze-bunted a run home with an 0-2 count in the seventh to give the Sox a 5-2 lead.

The Twins cut it to 5-3 in the bottom of the seventh on Jorge Polanco’s homer against lefty Aaron Bummer. Jimenez drove home Goins in the eighth to make it 6-3, and Alex Colome allowed a run in the ninth but still picked up his 24th save in 25 chances.