After Rafael Furcal drove in the first run of the big inning with a single, Schumaker scored Furcal and Roger Craig with a triple to make it 3-0.
Eight batters later, Schumaker came up again and this time delivered a run-scoring double, making it 10-0 St. Louis.
The outburst, during which St. Louis sent 17 men to the plate, also tied the Cubs record for most runs allowed in an inning.
Jake Westbrook (8-8) notched the win with seven shutout frames, shutting Chicago down on three hits and two walks while striking out five.
Cubs starter Matt Garza left after three innings with cramping in his right triceps.