Atlanta's 10-game winning streak is its longest since the club won 15 straight from April 15-May 2, 2000. The Braves are 12-1 and off to their best start since they began the 1994 season 13-1.
Eric O'Flaherty (3-0) allowed one hit and struck out two in a scoreless eighth for the win in relief.
Heyward's second homer, Upton's eighth and Uggla's third were solo shots off Kelvin Herrera (1-1), who gave up three hits, four runs and one walk in two-thirds of an inning. The Braves have outhomered opponents 25-7 and outscored opponents 68-25 for the best run differential in the majors.