Chris Davis also had a three-run homer for Texas, which took two of three from the club with the best record in the majors. Jason Grilli, C.J. Wilson and Frank Francisco combined for 5 1/3 innings of two-hit relief.
Neither starter let the other side hit the ball much, either — for different reasons.
A.J. Burnett (10-8) lost despite striking out a season-high 12 in six innings. Texas' Dustin Nippert was pulled after walking seven in 3 2-3 innings.
Through 7 1/2 innings, in fact, only 33 of 66 hitters overall managed to put the ball in play. By the end, the teams combined for 25 strikeouts and 11 walks.
Kinsler got Texas' first hit, a three-run homer in the fourth. Burnett retired the first 11 batters before walking Josh Hamilton and Nelson Cruz on full counts, bringing up Kinsler.
Catcher Jose Molina went to the mound to talk with Burnett, and Kinsler lined the next pitch over the left-field wall. Kinsler connected for a solo shot in the eighth, giving him a career-high 28 home runs.
Burnett fell to 0-4 in six starts this month. He was tagged for a career-high nine runs by Boston in his last outing and shook off catcher Jorge Posada several times, leading to talk they weren't on the same page.
Posada missed this game, a day after a foul tip bruised his left ring finger. The Yankees thought the injury might sideline him for a few days, and there was no timetable for his return to the lineup.
Davis launched a three-run homer in the seventh off Phil Coke. He also made a nifty play at first base to end the sixth after Derek Jeter's hard grounder bounced off his glove — Davis retrieved the ball and made a blind, backhanded flip to Grilli covering the bag.
Grilli (2-2) entered in the fourth, escaped a first-and-third jam by getting Alex Rodriguez on an easy comebacker and pitched 2 1/3 innings. Wilson went two innings and Francisco worked the ninth.
Texas, still in the thick of the pennant race, became the first team to win a series at Yankee Stadium since Washington won two of three from June 16-18.
Mark Teixeira hit a pair of early RBI singles for the Yankees, both times driving in runners who drew walks from Nippert and stole a base.
Notes
Kinsler has five multihomer games this year and seven in his career. … Texas has hit 190 homers, second in the majors to the Yankees' 195. … Texas' Michael Young extended his hitting streak to 14 games, the longest active string in the majors. … The Rangers have won seven straight rubber games on the road. … Tennis star Andy Roddick threw out the first ball. Known for his fastball serves, he went with a lob. A-Rod of racket fame waved at A-Rod of the Yankees before the ceremonial pitch. The U.S. Open starts next week.