Faried finished with 19 points and nine rebounds, and forward Danilo Gallinari had 25 points for the Nuggets (4-4). Guard Emmanuel Mudiay finished with 16 points and 11 assists.
Faried delivered the win when he grabbed an errant jump shot by Gallinari and put it in.
Milwaukee guard Khris Middleton missed a 20-foot jumper from the baseline that would have won it for the Bucks (4-5).
Guard Jerryd Bayless led Milwaukee with 22 points off the bench, and centre Greg Monroe had 18 points and 10 rebounds. Guard Greivis Vasquez added 15 points and nine assists.
Milwaukee led most of the game before falling behind by 13 early in the fourth. Bayless scored 11 points in a 13-2 Bucks run that cut Denver’s lead to 95-93.
Bayless tied it with a three-pointer with 1:54 left, and forward Johnny O’Bryant’s baseline jumper gave the Bucks a 100-98 advantage with 1:21 remaining.
Mudiay then split a pair of free throws to make it a one-point game before Milwaukee forward Giannis Antetokounmpo hit a soft jumper at the rim with 17.5 seconds left. Denver called timeout and set up the winning sequence.