Alex Rios went 2-for-2 with two walks, a double and a run scored, while Michael Choice and Leonys Martin also drove in runs for the Rangers, who snapped a three-game skid.
Matt Harrison (1-0) spun 5 1/3 innings of scoreless ball, allowing only three hits and four walks.
Nolan Arenado extended his hitting streak to a franchise-record 28 games with a single in the third. Brandon Barnes and Michael McKenry both doubled for the Rockies, who entered the game with wins in six of their last seven.
Franklin Morales (3-2) was belted for five runs -- four earned -- on six hits with three walks across six-plus innings in the loss.