Guard E'Twaun Moore was the Pelicans' leading scorer with 24 points and DeMarcus Cousins added 22 points, 16 rebounds and seven assists.
Atlanta (2-12) led 101-97 with 2:35 left when Tyler Cavanaugh hit an open 3-pointer, but Miller responded with a 3-pointer from the right wing and another from the top of the key with 52 seconds left to put New Orleans on top 106-104.
Kent Bazemore made one of two free throws to trim the deficit to 106-105. The Hawks had a chance to take the lead, but Dennis Schroder threw the ball away on the next possession.
The Pelicans (8-6) had the ball with 3.2 seconds left, but Anthony Davis threw the ball away, giving Atlanta one last chance with 0.7 of a second remaining. But Bazemore's 3-point attempt fell short.
Atlanta was paced by Bazemore with 22 points.
The Pelicans came out listlessly in the second half, and Atlanta took a 64-52 lead with three 3-pointers -- two by Cavanaugh -- in a 14-7 run in the first 2:30 of the third quarter.
New Orleans' Jrue Holiday began attacking the paint in the next three minutes, scoring three layups to cut the deficit to 67-61.
Jameer Nelson hit a 3-pointer and a layup to give New Orleans its first lead since early in the game at 78-77, but the Hawks, by shooting 14 of 30 from long range, led 80-78 after three quarters.
John Collins scored eight of Atlanta's first 12 points in the fourth quarter, and the Hawks led 92-89 with 6:17 left.
NOTES: Pelicans PG Rajon Rondo, who missed the first 13 games while recovering from a core muscle injury, played five minutes against the Hawks. He scored on a baseline layup eight seconds into the game and finished with two points and two assists. ... New Orleans coach Alvin Gentry hopes Rondo's playmaking ability will help the Pelicans cut down on their average of 17.6 turnovers per game. ... The Pelicans' starters -- particularly DeMarcus Cousins and Jrue Holiday -- have been guilty of committing too many first-quarter miscues. "You just can't make high-risk plays," Gentry said. "We're not Brett Favre. Let's be Tom Brady. Let's make the easy, simple ones." ... Atlanta coach Mike Budenholzer said the Hawks have been playing better than their record indicates. "I think there's a lot of things that have been positive, (we) just need those for the 48 minutes," Budenholzer said.