Rios was obtained this week in a trade with the Chicago White Sox and in his debut with the Rangers on Saturday drove in a run and scored another.
Against the Astros on Sunday, Rios scored twice and had an RBI double in the sixth to give the Rangers a 2-0 lead.
Texas won its seventh consecutive game, its longest such streak of the season, and has captured 12 of 13.
Perez (5-3) made the 17th start of his two-year career his best one, limiting Houston to a ninth-inning run on four hits with eight strikeouts.
Houston starter Dallas Kuechel (5-7) retired 13 men in a row to start the game, but Rios reached on an infield single in the fifth and scored the first run of the game on a double by Geovany Soto.
Texas broke it open with a four-run ninth with Jurickson Profar contributing a two-run single. It was the seventh straight road win for the Rangers, equaling the longest in the American League this year.