Young, who averaged 29 points a game in the first round of the playoffs, pushed the visitors to a 19-point lead with eight minutes remaining only for Atlanta to struggle down the stretch and barely hang on for the victory.
The Hawks grabbed a 1-0 lead in the best-of-seven Eastern Conference semi-final series with game two at Philadelphia on Tuesday.
The series winner will face Milwaukee or Brooklyn to determine a berth in next month's NBA Finals.
Bogdan Bogdanovic and John Collins each added 21 points for the Hawks while Clint Capella added 10 points and 11 rebounds for Atlanta.
Cameroonian center Joel Embiid started for the Sixers after missing the final game of Philadelphia's first-round series against Washington with a right knee injury.
Embiid scored a game-high 39 points with nine rebounds and four assists while Seth Curry added 21 points and Tobias Harris had 20 points and 10 rebounds and Australian guard Ben Simmons had 17 points and 10 assists.
Young, who also passed off 10 assists, scored 12 points in the first quarter as Atlanta jumped ahead 42-27 and he finished with 25 in the first half as the Hawks seized a 74-54 half-time lead.
Lou Williams, a former 76er, came off the bench to score eight points in a 17-0 Atlanta run from late in the first quarter to early in the second to give the Hawks a 53-27 advantage, the 76ers going almost six minutes without scoring.
"They hit us in the mouth to start the game," 76ers coach Doc Rivers said. "They were the more aggressive team. They were the more physical team. They got off to a better start."
But the 76ers fought back late, with an 11-0 Philadelphia run, capped by consecutive Embiid layups, pulling the hosts within 118-115 with 66 seconds remaining.
Bogdanovic sank a 3-pointer with 41.3 seconds remaining for a 121-115 Hawks lead, but Ben Simmons made a free throw and Tobias Harris made a steal and layup for the 76ers.
Embiid made a breakaway foul on Collins and the Hawks' standout added two free throws and followed with a 3-point play to give Atlanta a 126-118 edge with 16.5 seconds remaining.
"We'll certainly be watching film on that," Hawks coach Nate McMillan said of his club's late collapse.
"We just lost our composure in the second half. We didn't handle their pressure well. In the second half we gave them the ball. They make you pay when you turn the ball over.
"We're going to have to be sharper going down the stretch. We know we will have to be better in the next game because they will be more attacking than they were in the second half of this game."
Simmons added a free throw and Embiid followed with a rebound and a 3-point play, then Danny Green made a steal and Simmons made a dunk to pull the sixers within 126-124 before Bogdanovic hit two final free throws to seal Atlanta's triumph.
"We lost this game by allowing the other team to score 128 points," Rivers said.
Embiid is an NBA Most Valuable Player finalist who averaged 28.5 points and 10.6 rebounds this season for the Sixers.
Sunday's other scheduled NBA playoff contest was a first-round seventh game between the Dallas Mavericks and Los Angeles Clippers.