"It's a dream come true, no question about that," Greene said. "It took the nerves off pretty early when we got a little bit of run support. I didn't have to be perfect. It definitely helped."
The Yankees pounded Cleveland starter Justin Masterson for five runs in two-plus innings, providing the cushion that Greene needed to calm his nerves. Brian McCann, Ichiro Suzuki and Brett Gardner each stroked three hits as the Yankees won for the fourth time in five games.
"We're swinging the bats well," Yankees manager Joe Girardi said. "It's been up and down during the course of the season, but we're showing what we're capable of doing. I know our pitchers like it."
With closer David Robertson having pitched in three of the last four games, Betances -- voted to his first career All-Star Game via the player vote -- was asked to handle the last two innings. He pitched around a single, getting Nick Swisher to fly to right field for the final out.
"It's pretty cool," Betances said. "I was just trying to go out there and keep it the same."
The 25-year-old Greene was pressed into duty after the Yankees dealt left-hander Vidal Nuno to the D-backs on Sunday, receiving right-hander Brandon McCarthy in exchange. McCarthy will make his Yankees debut on Wednesday.
Greene's Minor League numbers weren't sensational, as he was 5-2 with a 4.61 ERA in 15 games (13 starts) at Triple-A Scranton/Wilkes-Barre, but he'd been sharp of late. This marked his fourth stint in the big leagues, and just his second appearance in a game.
"We've said all along, this kid has a lot of talent," Girardi said. "Sometimes it's just figuring out what makes you successful and how you have to pitch. I don't think he tried to do too much, and I think that's pretty impressive, too."
Greene was knocked around in his April 24 debut against the Red Sox in relief, allowing three runs in a third of an inning. He said that any jitters were dismissed after the second inning on Monday, and it showed in the results.
"Seeing a lot of familiar faces definitely helps, too," Greene said. "It was a little bit of a roller-coaster ride earlier in the season, but it feels good to be here."
Leaning on his sinker to produce ground-ball outs, Greene held the Indians hitless until Swisher homered with two outs in the fifth inning. Asdrubal Cabrera also had a run-scoring single off Greene, who permitted four hits in all, walking none with two strikeouts.
"It's the first time you ever see a guy," Swisher said. "He's always got the advantage first time through the lineup. I thought second time through, we started seeing him a little better."
Girardi even trusted Greene to work through trouble in the sixth, getting Carlos Santana to fly out representing the tying run. It is possible that Greene showed enough to earn another start.
"That's obviously going to be a topic of discussion," Girardi said. "We haven't made any decisions about what we're doing moving forward, but we'll figure it out here pretty quick."
Masterson didn't have his good stuff, tossing just 54 pitches over two-plus frames before Indians manager Terry Francona had seen enough. Cleveland's bullpen was excellent in relief, including three scoreless innings by Carlos Carrasco, but the damage was already done.
"It wasn't real fun after the first," Masterson said. "The first inning was real fun."
Brian Roberts and Gardner logged run-scoring hits in a three-run second inning, a frame that also featured a bases-loaded walk to Derek Jeter. The damage could have been greater if not for a sharp 3-2 double play turned by Santana at first base.
"We were a couple inches from scoring a whole bunch," Girardi said.
After Masterson exited in the third, Ichiro knocked home a run with an infield hit and Francisco Cervelli reached on a run-scoring fielder's choice.
With a tired bullpen, Girardi said that his plan was to go from Greene to David Huff for as long as he could. Huff worked an inning, so Betances needed to rattle off the last six outs. He proved to be just as dominant in the ninth as he has been earlier in the game.
"It didn't feel different, not today," Betances said. "I feel like the experience has helped me a lot. If you would have told me that last year, I'm not sure how I would have reacted. But this year, the experience has helped me a lot."