Right-hander Yu Darvish turned 26 on Thursday.
Kinsler and Michael Young have been teammates on the Rangers for 845 games, tied for the third-longest pairing in club history. Juan Gonzalez and Ivan Rodriguez were together for 1,060 games and Young and Hank Blalock were paired for 878 games, while Rusty Greer and Rodriguez were teammates for 845 games.
Hamilton's two home runs in Wednesday's 3-2 loss were the first of his career during the regular season in the Bronx. He did hit three here during the 2010 AL Championship Series.