Jarrod Saltalamacchia led off the inning with a single off Brian Duensing (0-1) and advanced to second on a sacrifice bunt by Elvis Andrus to set up Kinsler's 22nd homer of the season and his second of the game. Kinsler had leff off the bottom of the first with a solo shot.
Marlon Byrd had two hits and scored twice and Andrus drove in a run for Texas, which won for the first time in its last five games.
Rangers' starter Derek Holland went four innings, allowing three runs on five hits with four walks and four strikeouts.
Doug Mathis, Eddie Guardado, Darren O`Day and C.J. Wilson combined for six innings of scoreless relief and Dustin Nippert (1-0) pitched two innings of one-hit, shutout relief to get the win.
Starter Francisco Liriano went six innings, allowing three runs on five hits with three walks and six strikeouts for the Twins, who carried a three-game winning streak into the game.
Denard Span, Alexi Casilla and Nick Punto drove in the runs for Minnesota, Punto with a solo homer in the third inning.