When Brady connected with Wes Welker on a 99-yard TD pass with 5:44 remaining, it gave him 511 yards on the night, moving him past the team mark of 426 set by Drew Bledsoe on November 13, 1994 in a 26-20 overtime win over the Vikings.
Brady, who finished 32-of-48 passing and threw his first interception since last October, also topped his former record for longest pass in team history. That was a 91-yarder from him to David Patten in a contest against Indianapolis on October 21, 2001.
The pass to Welker, which came down the left sideline, moved the Patriots to a 38-17 lead, just after the Dolphins failed on a fourth down pass in the end zone.
"I only threw it 25 yards," Brady said. "It wasn't like I threw it 99 yards. Wes did all the work. I just put it out there for him."
Brady's 517 yards were also the most in Monday Night Football history. The record is 554 yards, set by Norm Van Brocklin of the Los Angeles Rams in a September 28, 1951 contest vs. the New York Yanks.