"This is a very good lineup that he just shut down," Yankees manager Joe Girardi said. "Probably our best pitching performance of the year."
Kuroda allowed only four balls out of the infield and just one runner past first base. He held Texas hitless until Elvis Andrus' infield single leading off the seventh, outpitching All-Star lefty Matt Harrison in a crisp duel at Yankee Stadium.
The right-hander walked two and struck out five in his fourth career shutout and second this season. He threw 74 of 109 pitches for strikes.
"When you've got a great lineup like that," Kuroda said through a translator, "you can't lose your focus until the end."
The surging Yankees won for the sixth time in seven games. They've taken the first two in a four-game set between the AL's top two teams.
"Man, these games are a lot of fun to play in," Swisher said.
Derek Jeter singled off Harrison (13-7) with one out in the seventh to start the New York rally. Alexi Ogando came in to face Swisher, who had cracked a go-ahead grand slam off Ryan Dempster in the series opener Monday night for his first homer since July 19 -- a drought of 61 at-bats.
This time, Swisher fought his way back from an 0-2 count and drove a payoff pitch to the back of the Yankees' bullpen in right-center for his 16th home run.
"I was hitting on sound at that point. I mean, he's throwing 100 mph," Swisher said. "That 3-2 count, I was just hoping he would throw another fastball."
The bubbly switch-hitter rounded the bases with a big grin, and New York was on its way to a seventh straight regular-season victory over the Rangers at home.
"I wanted to put velocity on Swisher, and he didn't beat him with it," Texas manager Ron Washington said.
Teixeira then lined a shot into the right-field stands for his 23rd home run.
Slowed by a lack of run support lately, Kuroda (11-8) won for the first time in four starts and lowered his ERA to 3.06. He gave up a clean single in the eighth to Michael Young, who was immediately erased on David Murphy's double-play grounder.
Kuroda then worked a 1-2-3 ninth to finish a gem that took 2 hours, 35 minutes.
"He's been really, really big for us and he could have a number of more wins. He's been the hard-luck guy for us this year," Girardi said. "That was his 11th win for us. Realistically, he could have 15 or 16 at this juncture."
Kuroda has six scoreless outings of at least seven innings, most in the majors. He became the first Yankees pitcher with two shutouts in a season since Mike Mussina in 2005.
"I was doing everything I could to match him," Harrison said.
Featuring a sharp slider, Kuroda worked around two walks in the first three innings and handcuffed the hard-hitting Rangers, who began the night leading the majors in batting average (.278) and runs (580). They were shut out for only the third time all season.
A no-hit buzz began to build in the sixth, when second baseman Robinson Cano made a backhand play on Mitch Moreland's one-out grounder. Kuroda then struck out Ian Kinsler and had retired 10 straight heading into the seventh.
Andrus led off with a grounder toward the middle, forcing shortstop Jayson Nix to make a diving stop near the edge of the outfield grass. With little chance to get the speedy runner, Nix struggled to get the ball out of his glove and tried a desperation throw that was late and wide.
Base hit, no question, and Kuroda received a warm round of applause from the crowd of 44,533. Andrus was stranded at third when Nelson Cruz grounded out.
"I had to regroup myself a little bit, but I (said), a complete game or a shutout is not really important here," Kuroda said. "The most important thing is for the team to win, and that's what we accomplished today, and that's why I'm happy."
Yankees 3B Alex Rodriguez had X-rays on his broken left hand. Girardi said the hand is "definitely better" and the brace will come off, but Rodriguez isn't quite ready to swing a bat yet. He will begin doing strengthening exercises. ... With slugger Mike Napoli on the disabled list, Texas signed C Koyie Hill to a minor league contract. He was assigned to Triple-A Round Rock. ... Luis Martinez went 0-for-3 in his first start behind the plate for the Rangers. He was recalled from the minors Saturday when Napoli went on the DL. ... Jeter extended his hitting streak to 10 games. He started at DH, with Nix at shortstop. ... New York has eight shutouts, matching its total from last season. ... Kuroda has four career complete games, all shutouts.