Nene's free throws with 26.6 seconds left in 117 victory over the Hawks at Pepsi Center.
The Hawks had a final shot with 3.5 seconds left as Zaza Pachulia caught an inbounds pass in the lane, but his layup was long and Denver secured the rebound.
Ty Lawson filled the stat sheet for the Nuggets with 21 points, six rebounds, and seven assists, while Al Harrington and Danilo Gallinari chipped in 19 points apiece for Denver, which improved to 3-2 on its current nine-game homestand.
Joe Johnson led all scorers with 34 points and Josh Smith added 33 to go with 13 rebounds and seven assists before fouling out in overtime. Kirk Hinrich netted 22 points as the Hawks dropped to 2-3 on their current six-game road trip.