Jon Lester's pitch count had reached its upper limits and the Cardinals took advantage in the sixth.
The Cubs starter was removed after walking Greg Garcia with two outs in the bottom of the sixth on 112 pitches. Pedro Strop came in for Lester to face left fielder Tommy Pham.
Pham, who had a hot road trip but struck out three times Friday, doubled over the head of Cubs center fielder Albert Almora to send home Garcia from first. Right fielder Magneuris Sierra then singled in Garcia for his first MLB RBI to give the Cardinals a 5-1 lead.