Moore finished with 160 passing yards and Reggie Bush adding a rushing touchdown for the Dolphins (3-7), who won a third straight game for the first time since a logging a five-game streak in 2008, when they won a division title.
The Dolphins haven't allowed a touchdown during their winning streak. The last TD scored against them came at the 5:58 mark of an Oct. 30 loss to the New York Giants.
The Bills, meanwhile, dropped their third straight game and fifth in seven contests.
Ryan Fitzpatrick went 20-of-39 through the air for 209 yards with a pair of interceptions.
NFL-leading rusher Fred Jackson was limited to just 17 yards on seven carries, but did catch five balls for 50 yards.
2014: The Year in Fashion [PHOTOS]
UPI Sports Results for September 19, 2014