MINNEAPOLIS — In the midst of their fourth straight dismal season, the Minnesota Twins got big performances Wednesday night from two players they hope will be building blocks for years to come.

Kennys Vargas homered for the second consecutive game and Trevor May earned his first major league victory in an 11-4 win over the Chicago White Sox.

On July 13, Vargas was batting cleanup for the World Team in the Futures Game at Target Field. The Twins called him up from Double-A New Britain on Aug. 1 and he’s been on a tear ever since.

Vargas drove in three runs Wednesday with an RBI single in the fifth inning and a two-run homer into the second deck in left field in the sixth. He has 31 RBIs since his call-up — third-most in the majors during that span.

“He has huge power, we know that,” said teammate Eduardo Nunez, who had four hits and two RBIs. “He’s learning how to keep his average high and learning how to play the right way, and he’s doing a great job for us. After he’s joined this team we’ve scored a lot more runs, there’s no doubt about it.”

The Twins led the majors in runs last month. Three games into September they’ve scored 20 more, and Vargas continues to be a big part of the offense.

“If (a pitcher) throws one up over the plate and Vargas swings in the right spot, it’s got a chance to go a long way, and that’s exactly what happened,” Twins manager Ron Gardenhire said of Vargas’ homer.

May (1-4) made his big league debut on Aug. 9, but control was a big problem in his first four starts, all losses. This time, he walked just one batter and threw first-pitch strikes to 15 of the first 17 he faced.

“Getting ahead is the name of the game, especially at this level. You can’t just get behind guys and expect to get poor contact or swings,” May said.

The right-hander allowed three runs and six hits while striking out six in five innings.

“Getting a win at all is a step in the right direction,” May said. “I made a couple more of those pitches I needed to make.”

The Twins broke loose for five runs in the fifth to break a 3-all tie and set up May for his milestone win. Vargas’ RBI single and Eduardo Escobar’s two-run triple did the bulk of the damage.

Minnesota jumped out to a 3-0 lead in the first behind Nunez’s RBI triple and back-to-back doubles from Josmil Pinto and Oswaldo Arcia.

White Sox starter John Danks (9-10) settled down to hold the Twins scoreless for the next three innings, and Chicago got back into it. Dayan Viciedo’s two-run homer into the second deck in left brought the White Sox within a run, and Adam Eaton’s RBI single tied it in the fifth.

The game was halted in the bottom half by a 16-minute rain delay. When play resumed, Vargas lined Danks’ first pitch into right field for an RBI single that gave the Twins a 4-3 lead.

Four batters later, Escobar hit Matt Lindstrom’s first pitch into the right-field corner for a two-run triple.

“I almost felt like every time I threw a fastball they knew it was coming,” said Danks, winless in his last seven starts. “We tried to mix it up and almost tried to pitch backwards a little bit. I worked better than before, but it was just an all-around bad night. It’s pretty frustrating.”

COMIC RELIEF

Nunez was running with the pitch from second base on Vargas’ base hit to right in the fifth. But he didn’t see where the ball went, so he slid into third before scrambling to his feet and making it home for the go-ahead run.

“He’s entertaining. That’s why we love the guy,” Gardenhire said. “He keeps us smiling.”

TWINS TIP CAPS TO KONERKO

The Twins honored White Sox captain Paul Konerko during a pregame ceremony commemorating his final game in Minnesota. First baseman Joe Mauer and closer Glen Perkins gave Konerko a bottle of wine, and Gardenhire presented a $10,000 check for the Bring Me Home Campaign, which supports foster care in Chicago.

In his 18-year career, Konerko played 256 games against the Twins, more than any player in history.

TRAINER’S ROOM

White Sox: Jose Abreu returned to the lineup at DH after being given a night off due to general soreness. “It’s nothing major,” manager Robin Ventura said. “I think at times it’s his ankle, at other times it’s his hamstring. When it all piles together he just doesn’t feel all that great.”

UP NEXT

The Twins open a four-game series against the Angels at Target Field on Thursday. Kyle Gibson (11-10) will look for his first win in his last four starts. He faces Hector Santiago (4-7).

The White Sox wrap up a short road swing with a three-game series in Cleveland that starts Friday. Chris Sale (11-3) pitches against fellow lefty T.J. House (2-3).