Burnett (1-0) blanked the Cards on three hits over seven innings, walking two and striking out seven in gaining his first win since coming to Pittsburgh in a February trade with the New York Yankees.
The 35-year-old had been on the disabled list since spring training. He fractured an orbital bone when he was hit in the face by a bunted ball during batting practice.
Pedro Alvarez drove in both Pittsburgh runs with a pair of RBI singles.
Jake Westbrook (2-1) yielded two runs on seven hits over 6 2/3 frames for St. Louis.