Talented guard Trae Young was dominant again for the Hawks, who trailed by 13 points at half-time before a strong fightback.
Young led the charge, finishing with 25 points, four rebounds and 18 assists, while John Collins did a strong job, with Clint Capela working hard on Embiid.
Embiid had an open look at a lay-up to put the 76ers up in the final minute but missed, along with Ben Simmons with a follow-up attempt.
Young added two points to give Atlanta a 103-100 lead with Philadelphia having the final possession, but Curry’s three-point attempt rimmed out.
Philadelphia coach Doc Rivers seethed at his side for a missed opportunity. He said: “Then we got back into the ball movement and went back to hero basketball.
“Basically everybody wanted to be the hero instead of trusting the team, trusting each other. When you do that you usually lose especially when the other team outworks you the whole f***ing game and that’s what they did today.”
Elsewhere, the Los Angeles Clippers also squared their series against the Utah Jazz after a strong first half helped them to a 118-104 Game 4 victory.
Kawhi Leonard starred with 31 points for the Clippers but finished the game on the bench after a collision which left him clutching his knee.
When asked post-game about whether the injury may impact his availability for the series, Leonard said: “Nah, I’ll be good.”
Leonard was supported well by Paul George who also had 31 points with nine rebounds, while Marcus Morris Sr had 24 points.