Their scores gave New England a 14-3 halftime lead.
Tom Brady threw for just 115 yards with 1 touchdown and 1 interception.
Moss and Wes Welker combined for 110 receiving yards on 9 receptions.
Maroney gained 81 yards on 23 carries, and Stephen Gostkowski booted a 30-yard, third-quarter field goal for the Patriots (9-5), who have beaten the Bills 13 straight times.
Buffalo's Ryan Fitzpatrick completed 17-of-25 passes for 178 yards with 1 touchdown and 1 interception.
Fred Jackson rushed for 80 yards on 15 carries.
Josh Reed caught 4 passes for 63 yards, and Rian Lindell kicked a 25-yard first-quarter field goal for the Bills (5-9), who have lost five of seven.
Notable deaths of 2014 [PHOTOS]