The Cardinals began the month of May on a winning note after having set a franchise record with 18 victories in April.
Chad Fox (0-1) was on the mound for his second inning of work when Aaron Miles led off the St. Louis 11th with a single. Fox unleashed a wild pitch, allowing Miles to go to second, and Brendan Ryan laid down a sacrifice that sent Miles to third.
Schumaker homered to right on the first pitch from Fox.
That made a winner out of Ron Villone (1-0), who gave up a hit in 2 1/3 innings of relief.
The Cubs lost for the fourth time in five games and fell 1 1/2 games behind the division-leading Cardinals.
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