NEW YORK — Shane Greene had little trouble finding the plate. Throwing to first was his problem.
The rookie right-hander wasn't the only player in pinstripes to struggle Monday night.
"It was an ugly game on our part," manager Joe Girardi said after the Yankees' first loss since the All-Star break. They were coming off a three-game sweep of Cincinnati.
Batting with more than 45,000 fans standing and cheering, Jeter sent an easy grounder to second baseman Rougned Odor and fell to 0 for 8 with a walk and two sacrifice flies with the bases full this year.
Miles Mikolas (1-2) then retired his final seven batters in winning for 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 his first three big league starts.
"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 yielded two runs, including Jacoby Ellsbury's homer, and four hits in a career-high 7 1-3 innings to outlast Greene (2-1) in a matchup of 25-year-old pitchers getting a shot because of injury-wrecked rotations.
Pitching for the first time at Yankee Stadium, Greene worked around three errors of his own — two on short tosses to first base — and one by second baseman Brian Roberts to work into the sixth with a 2-1 lead.
Matt Thornton relieved and gave up consecutive run-scoring hits to Odor and Choo, who helped Texas win for the third time in 17 July games.
"He was still throwing the ball well," Girardi said when asked why he left Greene in. "He gave up a broken-bat bloop hit over the third baseman's glove. It's not like they were hitting him hard."
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.
"I felt really good. I just had to keep on grinding," he said.
Jeter made an error at shortstop in the seventh to give the Yankees five in a nine-inning game for the first time since Aug. 20, 1998, against Minnesota.
"I don't think anyone is going to dwell on this one," Roberts said.
Adrian Beltre drove in the Rangers' first run with a fielder's choice in the third inning.
Slugging first baseman Mark Teixeira was not available to pinch hit in the ninth because he is out with a strained back muscle. Girardi said before the game Teixeira would miss at least three to four games.
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.
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.
NOTES: Rangers C Soto left after the top of the sixth with tightness in his right groin. 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. Rangers manager Ron 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.