Burnett (5-7) surrendered eight hits and a walk but used a pair of Pirates double plays to limit the damage. The right-hander broke a personal five-start winless streak, striking out nine while lowering his ERA to 2.73.
After Pittsburgh had built a 2-0 lead, Russell Martin cracked a three-run homer in the fifth to put the game and as the Bucs maintained a 1 1/2-game lead in the National League Central with their fifth win in seven contests.
Rockies starter Juan Nicasio (6-6) was tagged for four runs on six hits in a 4 1/3-inning effort.
Jonathan Herrera went 3-for-3 with an RBI for Colorado.