Perez (1-1), making his second start since being recalled from Class AAA Round Rock last week, allowed five hits and one walk while fanning three.
Tanner Scheppers threw a scoreless eighth despite surrendering a pair of hits and Joe Nathan closed out the victory with his 24th save as the Rangers racked up a fourth straight win.
Cards starter Shelby Miller (8-5) was touched for four runs on eight hits in a 5 2/3-inning performance.
Allen Craig and Shane Robinson each drove in a run for National League Central leaders.
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