NEW YORK -- Detroit Tigers reliever Shane Greene attempted to pick Jacoby Ellsbury off first base during a one-run game at Yankee Stadium in the ninth inning Tuesday.

His throw sailed low, and Ellsbury raced to third, putting the tying run 60 feet away.

By then, Greene couldn't help but laugh and think about the time he made three errors in one of his first starts for the New York Yankees.

Greene then shrugged off his errant throw and nailed down a five-out save as the Tigers held on for a 4-3 victory over the Yankees on Tuesday night. The 28-year-old right-hander was anointed closer Monday afternoon after Justin Wilson was traded along with Alex Avila to the Chicago Cubs.

"I kind of laughed in my head when I threw the ball away," said Greene, who made three miscues in his third career start July 21, 2014, against the Texas Rangers. "It brought back some memories with the three-error start here one time. I enjoyed it, and I'm glad I got the first one out of the way."

Greene recorded two saves last season, but this was his first opportunity to show he could be an effective closer.

"He's going to get the opportunity for sure," Tigers manager Brad Ausmus said. "I think people around the league know he's a pretty good relief pitcher. He's pitched in a number of roles."

The first four outs were relatively stress-free. Greene ended the eighth by getting Matt Holliday on a double play. He opened the ninth by retiring Chase Headley on a groundout and striking out Todd Frazier. Then the fun began.

Green fell behind Ellsbury and walked the pinch hitter, setting it up for Brett Gardner to deliver his third walk-off hit in the last five days. After the first pitch to Gardner, Greene made a low throw as Ellsbury slid back, but the ball sailed past first baseman John Hicks' glove into right field. Only a heads-up play by shortstop Dixon Machado prevented the tying run from scoring.

Following a visit to the mound by Ausmus, Greene intentionally walked Gardner. Gardner stole second on a 0-2 pitch to Clint Frazier, but on the next pitch, the game ended with a popup to Machado.

"It was tough, honestly," Greene said. "I was pretty excited for the opportunity, and then to do it here for me, it's a little extra special, full circle, and then it's kind of funny, I haven't thrown a ball away on a pickoff since I was a Yankee. Of course, I do it here. It was a lot of fun."

Said Yankees manager Joe Girardi: "You like your chances. We had a couple opportunities to score tonight and weren't able to do it, but you like your chances."

Before Greene helped Detroit escape with its fifth win in 13 games, Anibal Sanchez (3-1) turned in one his best outings of the season. In a season-high 6 2/3 innings, Sanchez allowed two runs and six hits before three relievers preceded Greene.

Hicks hit a three-run homer and Justin Upton added a solo homer off CC Sabathia (9-4).

Hicks, who is in his fifth stint with the Tigers, capped a 10-pitch at-bat in the second by hitting his fifth homer and first since rejoining the Tigers on Monday. Upton hit his 18th homer with two outs in the third.

Those homers spoiled Sabathia's 500th career start. Sabathia, who joined Bartolo Colon as the second active player to reach 500 starts, allowed four runs and six hits in six innings while struggling with command of his slider and changeup.

"Those two pitches didn't really do much for me," Sabathia said. "They were either just off the plate or getting too much of the plate."

Didi Gregorius drove in all three runs for the Yankees, who lost for the second time in nine games. Gregorius lined a two-run homer into the right field seats in the fourth and hit an RBI single in the eighth after Gary Sanchez singled and took second on an error by Upton in left field.

NOTES: RHP Sonny Gray will make his debut for the Yankees on Thursday in Cleveland, followed by LHP Jaime Garcia. ... Manager Joe Girardi said the Yankees are going with a six-man rotation just for this turn to give RHP Luis Severino an extra day after he threw 116 pitches Monday. ... Detroit SS Jose Iglesias did not play due to a sprained right wrist. He is day-to-day. ... Tigers DH Victor Martinez was given the night off after getting hit in the foot in the ninth inning Monday. ... New York OF Aaron Hicks (strained right oblique) will start a rehab assignment Wednesday. He could return by next week when the Yankees face the Boston Red Sox.