Beltre, who had two RBI in the victory, singled to right field with one out to break a 3-3 tie and send the Rangers on to their eighth win in nine games.
Beltre drove in Elvis Andrus in the ninth inning as the Ranger put the game on ice. Andrus scored three runs in the contest and also drove in a run.
Yu Darvish (11-5) earned the win for Texas with three runs on eight hits over seven innings. Tanner Scheppers was credited with his first save.
Kole Calhoun and Mike Trout hit back-to-back home runs for the Angels in the first inning. Kevin Jepsen (1-3) took the loss in relief of Garrett Richards, who turned in a quality six-inning start.