Lee homered during a four-run third inning that staked the Marlins to a 5-1 lead.
Burnett picked up the victory after giving up a run and four hits with two walks and four strikeouts over five innings. Four relievers pitched an inning apiece, including Miguel Tejera, who finished up for the save.
Woody Williams alowed five runs in four innings and took the loss.
William Ortega and Mike Coolbaugh each had two hits and scored a run for St. Louis.