Brady, who had been mired in a four-game slump, had little trouble against the Steelers' porous defense, completing 23-of-33 pass attempts as the Patriots rolled up a season-best 610 total yards of offense.
Rob Gronkowski made a career-high nine catches for 143 yards with a touchdown and Aaron Dobson complemented that performance with five grabs for 130 yards and two TDs.
Danny Amendola contributed 122 receiving yards with a score on four receptions for the Patriots (7-2), who remained undefeated at home.
Stevan Ridley led New England's ground game with two rushing touchdowns, gaining 115 yards on 26 carries.
Pittsburgh (2-6), meanwhile, surrendered the most points in a game in franchise history.
The lackluster defensive effort nullified a good game from Ben Roethlisberger, who amassed 400 passing yards with four TDs and two pick-offs on 28-of-48 efficiency.
Jerricho Cotchery hauled in three scoring strikes, finishing with seven catches for 96 yards.