Hiroki Kuroda was behind 4-0 after five batters and left fielder Brett Gardner will be out of the lineup for at least 15 days.

From beginning to end, it was a rough night for the New York Yankees.

Justin Morneau hit two mammoth homers off Kuroda, and Jason Marquis won his Minnesota debut with his healthy daughter in attendance to lead the Twins past New York 6-5 Wednesday night.

Robinson Cano hit his first home run this season and Derek Jeter his fourth before a crowd of 36,831 — the first below 40,000 at the new Yankee Stadium. Kuroda, however, was tagged for 10 hits in 4 1-3 innings after taking a shutout into the ninth Friday in the home opener against the Angels.

"He was up all night," manager Joe Girardi said. "He didn't have his good sinker tonight like he had with the Angels."

After the game, Girardi also said Gardner is headed to the 15-day disabled list with an injured right elbow.

Joe Mauer and Jamey Carroll each had an RBI double in a four-run first inning against Kuroda (1-2), helping the Twins improve to 9-34 at Yankee Stadium — including the playoffs — since Ron Gardenhire became manager in 2002.

Morneau hit a two-run shot in the first and a solo drive in the fifth that chased Kuroda.

"We weren't really able to kind of weather the storm there," Yankees catcher Russell Martin said. "Today was just one of those days where he seemed like he was struggling with command a little bit."

No doubt it was an emotional day for Marquis, who signed a $3 million, one-year contract with Minnesota in the offseason but left spring training after four starts when his 7-year-old daughter, Reese, was seriously hurt in a bicycle accident. Her injuries included a lacerated kidney and doctors initially were worried about whether she would survive. But she was released from the hospital on opening day and she sat in a Yankee Stadium suite Wednesday night after bouncing around the ballpark with her dad the day before.

"To see where she was a month ago is nothing short of amazing," Marquis said. "Lots of players have hardships in their careers. The challenge is to step onto the field and learn to try to separate it — go out there and play a kid's game."

Marquis (1-0) grew up in New York rooting for the Yankees and still lives in the city. He said he left about 50 tickets for family and friends for his first career start at Yankee Stadium.

"It was definitely exciting to play in this type of atmosphere," Marquis said. "Family and friends, you can't put a dollar amount on their support."

Morneau, the 2006 AL MVP, was derailed by a concussion as well as wrist and neck injuries the past two seasons. But he has four home runs in his last six games — matching his total in 69 games last year.

Morneau's drive deep into the raised right-field bleachers in the fifth gave the slugger his 15th career multihomer game and first since May 31, 2011, at Detroit.

No surprise that it came at the new Yankee Stadium, where he has seven home runs in 12 games. He has five homers in 80 games at Target Field in Minnesota.

"It looks like he's on everything right now," Martin said. "It's tough. He's a premium hitter. Definitely a tough out."

Morneau, who sat out Tuesday night for the first time this season, also singled and scored in the third on Sean Burroughs' first hit and RBI with the Twins.

Needing to build up arm strength and stamina, Marquis made two starts at Double-A New Britain before he was recalled Wednesday. During his time with the Rock Cats, the right-hander commuted about 130 miles each way to and from Connecticut so he could spend time with his daughter as she healed.

Marquis threw 87 pitches in five innings and left with a 6-4 lead. He earned his first major league win since July 18 with the Nationals at Houston.

Twins relievers Brian Duensing, Jared Burton and Matt Capps combined for four solid innings. Capps gave up Jeter's solo shot before fanning Curtis Granderson and retiring Mark Teixeira on a long fly for his third save.

"Got under it just a little bit. A hair lower and we're still playing," Teixeira said.

NOTES: Gardner was a late scratch after apparently getting hurt while making a tumbling catch Tuesday night. He was replaced by Andruw Jones, who is 9 for 13 with five homers and 14 RBIs against Marquis. ... New York will recall RHP Cody Eppley from Triple-A Scranton/Wilkes-Barre. ... With the Yankees in the midst of playing 13 straight days, 3B Alex Rodriguez was rested for the first time this season and Nick Swisher was the DH. Rodriguez grounded out as a pinch-hitter in the ninth. ... RHP Phil Hughes (0-2, 9.00 ERA) starts the series finale Thursday night against Minnesota RHP Anthony Swarzak (0-2, 3.75). With LHP Andy Pettitte on the way and RHP Michael Pineda on the mend, Hughes insisted he's not worried about losing his spot in the rotation if he doesn't start pitching well. "I have to do my job first," he said. "That's part of being a Yankee. If you're not getting the job done, then they'll bring in someone else."