CHICAGO -- During a Sunday morning team meeting run by White Sox manager Rick Renteria, Lucas Giolito was informed of being selected as an American League All-Star for the first time.

So, the right-hander added another goal to his list before taking the mound in a 4-3 victory over the Twins at Guaranteed Rate Field.

• Box score

“My mentality was 'All right, I was selected to the All-Star team. Let me go pitch like one today,’” said Giolito after becoming the first 11-game winner in the Majors this season.

Giolito might have put a special exclamation point on his All-Star selection, joining teammates James McCann and Jose Abreu for the special trip to Cleveland, if not for a rain delay covering 2 hours and 54 minutes. The right-hander was spot-on during his five innings of work, yielding a Jonathan Schoop single and nothing else, as he struck out four.

• Abreu, Giolito, McCann named All-Stars

Three relievers had to finish off the victory, with Aaron Bummer and Alex Colome keeping the Twins scoreless over the last three innings. But it was Giolito who set a new career high in victories while lowering his ERA to 2.72, with one start remaining before the break against the Cubs on Saturday.

“I was a little discouraged after they called us off the field there. I was feeling good,” Giolito said. “I wanted to keep going. The pitch count was down. But at the end of the day we got the W. The bullpen picked me up. I went five and dive, so they picked me up. It ended as a close game but a win is a win.”

Abreu, who was selected to his third All-Star Game and second straight, knocked out three singles, while McCann, chosen as an All-Star for the first time, singled home a run during a two-run sixth. Yoan Moncada features statistics deserving of All-Star recognition, but he settled Sunday for a two-run homer off of Minnesota starter Lewis Thorpe to give the White Sox a 2-0 lead in the third.

Moncada has 14 homers and 44 RBIs this season, and his three hits raised his average to .304 at the end of June.

“He’s a good player,” said Abreu of Moncada through interpreter Billy Russo. “Everyday, he works hard and he goes out there to try to do his best. To make the adjustments, day by day, pitch by pitch, and that’s something that is a difference in him from the player he was last year. He’s an All-Star.”

Sunday’s victory gave the White Sox a series win against a Twins squad holding a 13-game-lead over the South Siders in the AL Central and sitting at 53-30. It was a much different weekend from May 24-26, when the White Sox were swept at Target Field.

“Taking two out of three is a big weekend, especially heading into an off-day, leaving on a high note and go enjoy tomorrow with that victory under our belt,” McCann said.

“The record right now is [39-42] and that speaks good about us,” Abreu said. “That’s because we are improving. We are getting better and we’re very, very close to be a good team, and a team that can be in the playoffs and to be considered one of the teams to win a championship.”