Brady, who completed 21-of-22 passes for 258 yards, scored on a 1-yard run in the second quarter and hooked up with Moss on a 14-yard TD in the third.
Wes Welker, back in the lineup after missing two games with a knee injury, caught six passes for 48 yards for New England (3-1).
Joe Flacco was 27-of-47 for 264 yards, including touchdown throws of 20 and 13 yards, for the Ravens (3-1).
Derrick Mason led Baltimore's receivers with 88 yards and a touchdown.
Celebrity Breakups and divorces of 2014 [PHOTOS]