Bradley used a nice individual effort to tie the match in the 53rd minute after receiving a pass near midfield. He shielded his defender down the field, beat two more Revolution players and sent a shot inside the far post.
"To be able to actually get that shot on goal and into a corner after that run is incredibly impressive," said TFC head coach Greg Vanney.
Toronto FC (3-5-1) held off several late chances by New England (5-2-4).
Andy Dorman got past the defence in the 85th minute for Lee Nguyen's through ball, but Toronto goalkeeper Chris Konopka came out of his area to block a low shot. Nguyen had a shot go just wide one minute later and Diego Fagundez narrowly missed a header in the 93rd.
"Chris was massive," said Vanney. "He grinded it out like a man and he made some big saves for us, he was big, he was an important factor tonight."
New England extended its undefeated run to nine games — the Revolution's longest since 2005. Charlie Davies had his four-game scoring streak ended.
Juan Agudelo's header in the 32nd minute gave New England a 1-0 lead. After a defensive turnover, the Revolution used a nine-pass sequence to set up London Woodberry's curled cross to Agudelo at the far post.
Toronto's Jozy Altidore was subbed out in the 21st minute with an apparent leg injury. He raced to get a through ball in the box, slid a pass across goal and immediately signalled to the bench for a sub. The Revolution's Jermaine Jones left the game in the 63rd minute.
"I don't have a real indication of what exactly, or how bad, or potentially how long but when I just saw him he was in good spirits for the guys because the guys grinded it out," Vanney said when asked for an update on Altidore's status. "We'll figure out the details later tonight, tomorrow for him."