The teams were tied at 98 when the Pelicans' Brandon Ingram, who had 20 points, attempted a transition 3-pointer for the lead but missed the rim entirely.
Atlanta went in front for good shortly after, when John Collins came straight down the lane unimpeded to put back Young's missed 3-pointer off the back rim with a dunk with 55 seconds left.
New Orleans still had several chances to retake the lead in the final 10 seconds after Young missed another shot from deep. But Clint Capela stopped Devonte' Graham from converting a transition layup, and after New Orleans rebounded and called timeout, Ingram again missed the rim with a pull-up jumper. Pelicans rookie Trey Murphy had two hands on the rebound of Ingram's miss, but the ball bounced off his leg and out of bounds with 1.5 seconds to go, and Young hit two free throws for the final margin.
Collins had 16 points and 12 rebounds for the Hawks, who've begun the season with three victories in their first four games. De'Andre Hunter scored 13 points, Bogdan Bogdanovic added 12 and Capela had 12 rebounds and four blocks.
Graham hit five 3s and led New Orleans with 21 points. Jonas Valanciunas added 16 points and 15 rebounds for New Orleans, which has lost four of its first five games without star forward Zion Williamson, who is recovering from offseason foot surgery.
The Pelicans led by as many as 16 points in the first quarter when Kira Lewis' layup made it 33-17.
That lead was almost entirely gone less than halfway through the second quarter when Hunter's 3 made it 43-41.
Valanciunas' free throws, followed by Graham's 3 in the final second of the period, gave the Pelicans a 59-53 lead at halftime. But New Orleans turned the ball over five times and missed 10 of 18 shots in the third quarter, allowing Atlanta to surge into the lead.
The Hawks closed the third quarter on a 12-2 run that started with Young's 3 and ended with Delon Wright's pull-up from deep to take an 84-77 lead heading to the fourth.
John Collins and Trae Young lead the Hawks to their third win in four games.
Hawks: Scored 52 points in the paint and 19 second-chance points. ... Outrebounded New Orleans 55-44.
Pelicans: Guard Garrett Temple injured his ankle in the first half and did not return after scoring six points in nine minutes off the bench. ... Starting guard Nickeil Alexander-Walker missed 11 of 14 shots and missed all seven of his attempts from deep.
Hawks: Visit Washington on Thursday night in the second stop of a three-game road trip.
Pelicans: Host Sacramento on Friday night in the second of three straight at home.
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