Brady's milestone toss -- a 34-yarder to newly acquired wide receiver Josh Gordon -- came with 9:39 remaining and gave New England a 31-17 lead. Brady was 34-of-44 passing for 341 yards with three touchdowns and two interceptions.
Brady joins Peyton Manning (539) and Brett Favre (508) in the exclusive club. New Orleans' Drew Brees (496) could become the fourth member as early as Monday when the Saints host the Washington Redskins.
Brees, who turns 40 in January, and Brady, 41, appear likely to pass Manning. Brady has said that he hopes to play through the 2022 season.
"I think 45 is a pretty good number for right now," Brady told ESPN in 2017. "I know the effort it takes to be 40. ... My love for the sport will never go away. I don't think at 45 it will go away.
"At some point, everybody moves on. Some people don't do it on their terms. I feel I want it to be on my terms. I've got to make appropriate choices on how to do that, how to put myself in the best position to reach my long-term goals."