Pittsburgh scored four times over the first two innings, with two of the runs being unearned, and Burnett (8-2) threw shutout ball while striking out four.
Four relievers teamed to go the final three innings with Joel Hanrahan striking out two in the ninth for his 18th save.
Doug Fister (1-4) made his second start for the Tigers since coming off the disabled list and was at least partially undone by his own throwing error.
With two on and one away in the Pittsburgh second, Burnett hit a grounder back to Fister and he threw the ball away at first. That allowed one run to score and another run came in when left fielder Delmon Young made a wild throw back to the infield.