MINNEAPOLIS -- Coming in after an early deficit, four relievers gave the New York Yankees a big boost in Minnesota on Tuesday with 5 1/3 scoreless innings.

The organization then gave the bullpen a big lift.

Didi Gregorius had three hits, including a two-run homer in a five-run fifth inning, and New York spoiled Bartolo Colon's Twins debut in a 6-3 victory over Minnesota on Tuesday.

Following the game, the Yankees acquired relievers David Robertson and Tommy Kahnle, along with third baseman Todd Frazier, from the Chicago White Sox in exchange for struggling reliever Tyler Clippard and three prospects.

"We're in a tough stretch where we're not playing great and we go out there and make a move still, that makes you feel like the front office and the team believes in us," New York third baseman Chase Headley said after the game. "So, hopefully we can play the way that we have most of the season now."

The Yankees showed a bit of the promise they hold after a slow start on Tuesday.

Ronald Torreyes added three hits for New York. Aaron Judge had two hits, a walk, two runs and an RBI, and Gary Sanchez added two hits and two RBIs for the Yankees, who have won 11 of their past 14 games against Minnesota.

"It should tell them, 'Hey, we're in this, and we need to continue to play and play hard and play better than we've done,'" New York manager Joe Girardi said. "But it should be a pick-me-up in there in a sense, like, 'Hey, there's a lot of people who believe in this club.'"

At the start, all eyes were on the 44-year-old Colon, who signed a minor league contract with Minnesota earlier this month after being released by the Atlanta Braves. The Twins are the 10th team Colon has pitched for in his career, and Minnesota was hoping he could help stabilize the back of the rotation.

Colon (2-9) gave up four runs on eight hits in four-plus innings, his ERA rising to 8.19 in 14 major league starts this season.

"A lot of two-seamers," Colon said, through an interpreter, of his approach. "I didn't get that feel for it when I was with Atlanta."

New York's bullpen stabilized the game after starter Luis Cessa couldn't get through the fourth inning, and the Yankees' offense finally awoke from a post-All-Star-break slump.

Chasen Shreve (3-1) yielded two hits in 1 1/3 scoreless innings. Adam Warren didn't allow a baserunner in two innings, Dellin Betances survived a hit and a walk in one inning and Aroldis Chapman secured his 10th save in 13 chances.

The Twins left 12 runners on base and were 2-for-18 with runners in scoring position.

"We had four or five chances with less than two outs and a man on third and I think we failed on every opportunity," Minnesota manager Paul Molitor said. "Those are the things you need to do if you want to win those games."

The early impressions of Colon's return to the American League were positive as he allowed only two hits through the first three innings and struck out Judge, Sanchez and Matt Holliday in that span.

The hits started falling in the fourth, though, and the 20-year veteran couldn't get an out in the fifth.

Judge led off the fourth with a single and came home on Headley's single. Torreyes, Brett Gardner and Sanchez started the fifth with consecutive hits to chase Colon after four-plus innings. Sanchez's double plated Torreyes and Gardner.

"I liked how he changed speeds on his fastball and I thought he got in on the guys he was supposed to get in on and back-doored the guys he was supposed to," Molitor said. "But like I said, it could've turned out better, that's for sure."

The Yankees' fifth-inning rally continued as Judge singled off reliever Ryan Pressly. Two batters later, Gregorius lifted his 12th homer of the year.

New York's offensive surge took Cessa off the hook after the right-hander surrendered three runs on four hits and four walks.

Cessa walked the first two batters he faced in the game, hit Miguel Sano with a pitch and later walked in a run in the first.

Sano hit a hard liner off Cessa to the bullpen in left-center field for his 22nd homer of the season in the third, and Brian Dozier's RBI triple off the out-of-town scoreboard in right field added a run in the fourth.

NOTES: New York 2B Starlin Castro was given the day off for rest, manager Joe Girardi said. OF Jacoby Ellsbury was out of the lineup as well as Girardi manages some days off for his outfielders. He said OF Aaron Judge would be held out of Wednesday's lineup to give him two days off heading into the weekend series at Seattle. ... New York optioned RHP Bryan Mitchell to Triple-A Scranton/Wilkes-Barre to make room for Tuesday's starter, RHP Luis Cessa. ... Minnesota RHP Phil Hughes was placed on the 60-day disabled list with a recurrence of symptoms of thoracic outlet syndrome. Hughes had surgery last season to remove part of a rib to alleviate the symptoms, but manager Paul Molitor said he could he headed to another surgery. ... Placing Hughes on the 60-day disabled list made room on the 40-man roster for Tuesday's starter, RHP Bartolo Colon. ... The Twins activated LHP Craig Breslow (left thoracic rib soreness) from the disabled list and optioned 1B/DH Kennys Vargas to Triple-A Rochester.