NEW YORK -- Miles Mikolas didn't need to look into the batter's box to know who was stepping in with the bases loaded in the fifth inning. The roaring crowd said it all.
Mikolas got Jeter to ground into a double play, then pitched smoothly into the eighth inning Monday night to lead the Texas Rangers to a 4-2 victory.
"That's a big situation, a big jam to get out of," Mikolas said. "It almost makes me as a pitcher want to compete a little harder, let the fans down."
Mikolas (1-2) slapped his glove and pumped his fist twice while letting out a shout of approval as he left the field. Then he retired his final seven batters.
Mikolas' mom, fiance, sister and stepdad led a group up from Florida to see him win for the first time since Aug. 21, 2012, with San Diego. Mikolas won twice in 25 relief appearances for the Padres that year. He's had little success this season, coming in with a 10.05 ERA in three starts.
"I think that really relaxed him," Rangers manager Ron Washington said of the double play.
"It was an ugly game on our part," manager Joe Girardi said.
Second baseman Brian Roberts and Jeter, the shortstop, made the other errors for the Yankees, who had not committed five in a nine-inning game since Aug. 20, 1998, against Minnesota.
Mikolas yielded two runs, including Jacoby Ellsbury's homer, and four hits in a career-high 7 1/3 innings to outlast Greene in a matchup of 25-year-old pitchers getting a shot because of injury-wrecked rotations.
"I felt once he kind of got rolling, once he got some confidence, especially in an environment like this, you can get rolling," Roberts said of Mikolas.
Winners of only five of their last 25 games, the Rangers then broke through against Greene in his first appearance at Yankee Stadium.
Soto struck out with runners on first and third in the second -- they were there thanks to two poor throws to first base by Greene -- but came through with the tying hit in the sixth, a single to left after Jake Smolinski singled and Jim Adduci walked.
"He was still throwing the ball well," Girardi said when asked why he left Greene in so long. "He gave up a broken-bat bloop hit over the third baseman's glove. It's not like they were hitting him hard."
Matt Thornton relieved and gave up consecutive run-scoring hits to Odor and Choo.
Playing the outfield for the first time since the All-Star break because of left ankle trouble, Choo snapped an 0-for-22 skid with a third-inning double.
Green was charged with four runs and five hits in 5 2/3 innings. He had given up just two runs total in his first two career starts.
Carlos Beltran put New York ahead with a sacrifice fly in the first after Jeter walked, advanced to second on a balk and third on Ellsbury's single.
Ellsbury homered leading off the fourth to give the Yankees a 2-1 lead. It was the seventh straight time he reached base after going 4 for 4 with a walk in a win over Cincinnati on Sunday.
Rangers C Soto left after the top of the sixth with tightness in his right groin. He said he will see how it feels Tuesday before deciding if he can play. Smolinski bruised his left foot and was lifted for a pinch hitter in the ninth. ... Rangers RF Alex Rios (sprained right ankle) missed his second straight game. Washington said Rios looked much better and could play before the series ends Thursday. ... Injured Yankees LHP CC Sabathia (knee) turned 34. ... Up next: The Rangers plan to activate RHP Nick Martinez (1-6) from the DL to start Tuesday against the Yankees. He has been out since July 2 with discomfort on his left side. Rookie RHP Chase Whitley (4-3) starts for New York.