Foye played nearly 39 minutes in the game and hit 7-of-12 tries from 3-point range.
Ty Lawson had 19 points plus 13 assists for the Nuggets, who won their third in a row and handed Boston their eighth defeat in nine tries.
Jerryd Bayless scored six points off the bench in his first game for the Celtics since being acquired from Memphis in a three-team trade that also involved Oklahoma City.
The Nuggets shot 51.8 percent from the field while Boston struggled with 38.5 percent from the field. Denver also won the rebounding battle 56-35 and hit 14-of-31 shots from 3-point range.