Orlando's Jameer Nelson forced the first overtime by hitting a jumper with 11 seconds left in the fourth period. Mike Dunleavy kept Chicago in the game by nailing a 3-pointer with 13 seconds left in the first extra period and Glen Davis connected on a 3-pointer for Orlando with five seconds remaining in the second overtime.
Snell's jump shot in the final minute of the third extra session gave Chicago a one-point lead and, after Davis missed a 3-pointer for the Magic, Jimmy Butler hit two free throws for the Bulls to account for the final score.
Butler played 63 minutes, the most ever for a Chicago player in a regular-season game.
Noah scored 26 points and had 19 rebounds to lead the Bulls, Carlos Boozer added 23 points and Butler scored 21.
Orlando was led by 35 points from Victor Oladipo and 31 from Nelson.
The teams combined to attempt 217 shots and they collected 111 rebounds.