The Sixers had led by 18 points at one stage of game four.
The Sixers started strong and held a 60-42 lead with 1:43 left in the first half, but Bogdan Bogdanovic and Trae Young kept chipping away at the State Farm Arena.
Young landed a jump shot with 1:17 left to play to put the Hawks up 99-98 and finished with a 25-point haul, while Bogdanovic added 22.
Sixers star Joel Embiid missed a layup with nine seconds to play and only made four out of 20 field goal attempts.
The Clippers outscored the Jazz 30-13 in the first quarter, with Kawhi Leonard and Paul George both scoring 31 points each in the win.