With exactly six weeks left in the season and the Angels in desperate need of a win over the team they are trying to catch in the American League West, Kinsler came through with a clutch hit to break a 2-2 tie.
Texas has won 11 out of 13 and the Angels have lost five straight, allowing the Rangers to increase their division lead to a season-best seven games. Texas moved to 20 games above .500 and trails the New York Yankees by 31/2 for the best record in the American League.
Texas loaded the bases with nobody out against Ervin Santana (9-9) in the eighth, but the Los Angeles starter then struck Yorvit Torrealba and Endy Chavez. That brought up Kinsler and Santana quickly got two strikes on the Texas leadoff man. Needing only one more good pitch to escape the inning, Santana gave up a single to left that scored Nelson Cruz and Mike Napoli.
C.J. Wilson (12-5) went seven innings to get the win, giving up two first-inning runs on seven hits.
Los Angeles closed within one in the eighth on a homer by Howie Kendrick off Koji Uehara and Mark Trumbo singled to open the ninth against closer Neftali Feliz. Trumbo moved around to third on a pair of groundouts, but Erick Aybar flew out to right to end the game.
It was the 24th save for Feliz.
The teams close out a four-game series Thursday and will meet three more times in Texas next week.