With 3.5 seconds remaining, Young took the inbound pass from Kevin Huerter and dribbled past Jimmy Butler before sinking the short, soft jumper for the lead with 0.1 seconds remaining.
Butler missed a long attempt as the final buzzer sounded.
Taurean Prince had 23 points for Atlanta.
Joel Embiid had 27 points and 12 rebounds, and Butler had 25 points for Philadelphia.
The 76ers began the night with a solid hold on third place in the Eastern Conference, 3½ games ahead of Indiana and four games ahead of Boston. Philadelphia's six-game winning streak included a win over Boston on Wednesday night.
Huerter's steal from Embiid and jam gave Atlanta a 122-121 lead. Another turnover by Embiid, this time on a pass, set up an Atlanta fast-break opportunity which Young couldn't convert. Young fouled Butler, who made two free throws.
Young's long 3-pointer gave Atlanta a 125-123 lead, but Butler tied the game with a basket. Then, with 39.9 seconds remaining, Butler sank two free throws to give Philadelphia a 127-125 lead. Prince answered with a tying layup.
The Hawks were left with 3.5 seconds after the 76ers' 24-second violation, with Butler's miss waved off as coming too late
After snapping Utah's five-game winning streak by beating the Jazz 117-114 on Thursday night, the Hawks dropped another streaking playoff-bound team.
Atlanta led 74-68 at halftime and stretched the lead to 12 points, at 97-85, on Alex Len's three-point play. The 76ers closed the gap with 10 straight points and pulled even at 100-all on JJ Redick's 3-pointer to end the third period.
Embiid posted his 16th straight double-double and 54th overall this season. He had 37 points and a career-high 22 rebounds in the win over the Celtics on Wednesday night
76ers: C Boban Marjanovic, left unguarded in the corner, sank his first career 3-pointer in the first quarter. It was only the fourth career 3-point attempt in six seasons for the 7-foot-3 native of Serbia. ... The 76ers made 13 of 20 shots (60 percent) from the field in the first quarter. ... T.J. McConnell left the game with a bloody nose late in the third period. Coach Brett Brown was upset there was no foul called, even after a video review, on contact which caused the bloody nose. McConnell returned midway through the fourth.
Hawks: Young had 11 assists. ... Atlanta matched its season high for most points in a first half. The Hawks also scored 74 points in the first half against Miami in a 123-118 win on Nov. 3. The 74 points were the most allowed in a first half by the 76ers this season.
76ers: At Orlando on Monday night.
Hawks: At New Orleans on Tuesday night.