Rios also homered as the Rangers snapped a three-game losing streak.
Elvis Andrus provided two RBI as Texas remained 1 1/2 games behind American League West-leading Oakland.
Reliever Alexi Ogando (6-4) was credited with the decision with 1 1/3 scoreless innings after starter Nick Tepesch had yielded two runs on four hits in 3 1/3 innings.
The loss was hung on the Angels' Michael Kohn (1-2).
Andrew Romine delivered a two-run double for the losers.