Despite the strain of a trying season, Twins manager Ron Gardenhire hasn’t lost his appreciation for gallows humor. Sunday, he said a member of the team’s staff had recommended he reserve a lower-floor hotel room for the Twins’ upcoming road trip, so he wouldn’t hurt himself if he jumped.

Gardenhire smiled even more broadly after a 4-3 victory over the White Sox ended a three-game losing streak at Target Field. Coming out of the All-Star break, the Twins believed they could show they are not trudging down the road to a fourth 90-loss season in a row. A 10-game homestand was supposed to be their chance to prove it — and to convince General Manager Terry Ryan not to break up the roster.

With both their starting pitching and their offense floundering, the Twins completed the homestand 3-7 and sit 10 games below .500. Sunday’s victory gave them a sorely needed emotional boost. Behind six solid innings from starter Yohan Pino, the Twins took an early lead, lost it and scrapped their way back to dodge a sweep by their Central Division rivals.

Sam Fuld’s two-run single in the seventh inning put the Twins ahead 4-2 before White Sox catcher Adrian Nieto homered in the eighth. Twins closer Glen Perkins loaded the bases in the ninth, then struck out Alejandro De Aza and got Gordon Beckham to fly out to Fuld to end a game as dramatic as it was cathartic.

“It’s been really frustrating around here,’’ Gardenhire said. “It’s been a very disappointing homestand, but to get the win [Sunday] was huge. There was a lot of relief.’’

There were wide swaths of empty seats Sunday in a crowd announced at 27,818, testament to a grumpy fanbase becoming ever more critical of Twins players and management. Ryan voiced support for Gardenhire, saying he is “holding it together.’’ Ryan also said he will not bend to pressure to recall players and will bring up only those he deems superior to players currently on the roster.

Still, he acknowledged the gravity of the Twins’ situation. Weak starting pitching has put them in early holes, and their hitters have often appeared overmatched. Though injuries have also hurt, Ryan said the Twins cannot use that as an alibi, because successful teams find a way to rise above them.

“We’ve got to get back to competitive baseball,’’ Ryan said. “We’re going the wrong way. People expect you to at least have a relevant ballclub, and right now, we’re struggling in that area.’’

Gardenhire said the Twins’ top task is to shore up the starting pitching, which would take pressure off an overtaxed bullpen and stop forcing the offense to play from behind. Though he noted that some players are frustrated with their swings, he praised his team’s work ethic.

Perkins said the Twins’ mental state remains strong as well. He contends that the Twins are not a bad team, but an inconsistent one that is capable of better. With the home stand now a lost opportunity, he said the Twins have no choice other than to keep plugging away.

“Winning one isn’t a great consolation prize, but it’s better than losing,’’ Perkins said. “Hopefully, it will give us a little momentum.

 “It hasn’t gone the way we wanted it to go. But we have to keep going out and playing hard. That’s all we can do.”