New England (3-2-2) extended its undefeated streak to five games.
Cristian Maidana struck a free kick that glanced off the post to give Philadelphia (1-4-3) a 1-0 lead in the 42nd minute. New England goalkeeper Bobby Shuttleworth had only conceded one goal in the last four matches.
The Revolution's Charlie Davies tied it in the 64th minute. Bunbury beat his defender at the edge of the 18-yard box and delivered a ball to the far post where an unmarked Davies tapped it in. Bunbury put the Revolution in front 2-1 in the 76th minute. Diego Fagundez, a sub in the 71st, raced down the right sideline and placed a perfect cross to a striding Bunbury.
"I always try to contribute as much as I can, whether I'm starting or coming off the bench," Bunbury said. "It was a great effort from all of the guys. The whole 90 minutes, we didn't stop. I'm really proud of everybody."