Joe Johnson scored 34 points and Josh Smith had a season-high 33 points and 13 rebounds for the Hawks, who had a chance to win it at the buzzer.
Trailing by one with 3.5 seconds left, Atlanta got the ball to Zaza Pachulia at the foul line with. He drove the open lane before Danilo Gallinari rotated over, and Pachulia missed a layup off the glass as time expired.
Gallinari had 19 points in his best game since returning from a severely sprained left ankle.
Johnson took control in overtime after Smith fouled out, scoring seven straight points in overtime to give Atlanta a 117-112 lead. However, Denver came back and took a one-point lead on two free throws by Nene with 26 seconds left.
Without Smith in the game the Nuggets blanketed Johnson on the final play.
Before the game Hawks co-owner Bruce Levenson tried to dispel trade rumors surrounding Smith, saying "the likelihood of us trading Josh at the trade deadline is as close to zero as you can get."
Smith's play wasn't impacted by the rumors or Thursday's trade deadline, especially in the fourth when he scored 15 points and put the Hawks ahead 104-102 with 29 seconds left.
Lawson drove the lane but his layup went off the side of the rim with 15 seconds left. An Atlanta turnover with 9 seconds left gave Denver another chance, and Gallinari made a 3-pointer as he fell out of bounds to give Denver a 105-104 lead with 3.9 seconds left.
Hinrich was fouled and hit 1 of 2 free throws with 1.1 seconds left to send it to overtime. Hinrich finished with 22 points.
Atlanta's outside shooting kept the game close for most of the first half. The Johnson had 15 points and Smith scored 13 for the Hawks, who hit 8 of 14 from behind the 3-point line before intermission.
The Nuggets countered with a balanced scoring attack that had four players in double digits at the break.
Lawson led the way with 12, including two 3-pointers in the final 62 seconds of the first half to help the Nuggets extend the lead to 64-55.
NOTES: Smith's career high is 38 set Nov. 17, 2007, vs. Milwaukee. ... Hawks G Willie Green (back spasms/right hamstring) did not play and F Ivan Johnson was not with the team due to personal reasons. ... Nuggets F Kosta Koufas was dressed but did not play. He has missed six games with a strained left knee.