The long scoring play gave the Patriots the lead and they held on for their third straight victory.
Brady connected on 25-of-37 passes for 332 yards and an interception, Moss had six receptions for 147 yards and Wes Welker turned in nine catches for 84 yards.
Laurence Maroney ran 1 yard for a touchdown and Stephen Gostkowski booted field goals of 30, 38, 34 and 40 yards for the Patriots (6-2)
Ricky Williams ran 15 yards for a touchdown and Ronnie Brown passed 1-yard to Joe Haynos for another score for the Dolphins (3-5).
Miami quarterback Chad Henne completed 19-of-34 passes for 219 yards, with an interception.