Brady agreed Thursday to a 4-year contract deal worth a reported $72 million and wasted little time putting it into effect for the Patriots (1-0), going 25-of-35 for 258 yards.
Wes Walker made a triumphant return to New England after missing part of last year with a torn knee ligament, hauling down eight receptions for 64 yards and two-first half touchdowns.
Randy Moss contributed five receptions for 59 yards and Fred Taylor piled up 71 yards rushing on 14 carries in New England's season-opening win.
Cincinnati's Carson Palmer completed 34 of 50 pass attempts for 345 yards, with 12 of them going to Chad Ochocinco for 159 yards and a touchdown.
Terrell Owens' first game with the Bengals (0-1) featured seven catches for 53 yards.