Derek Holland (11-4) allowed three runs on nine hits and struck out seven in 8 2/3 innings.
Mitch Moreland was 3-for-5 with two RBI for the Rangers.
Angels starter Tyler Chatwood (6-9) faced only 16 batters. He gave up two runs in the first inning and three in the third.
Peter Bourjos and Torii Hunter each had two hits and one RBI got the Angels.
The defeat was the fourth in a row for Los Angeles, which slid to six games back of the Rangers in the AL West.
Texas has won five consecutive games and eight of its last nine.