The 76ers' Michael Carter-Williams nailed a 3-pointer to tie the score with 11.3 seconds left, but Irving responded with a last-second shot, giving him 39 points for the game.
On the play, he got free of two defenders, drove past Carter-Williams and converted the left-handed lay-in.
Irving's decisive basket made up for missing potential game-winning scores at the end of regulation and in the first overtime.
The Sixers' Thaddeus Young forced overtime with a layup with 5.5 seconds remaining in regulation.
Evan Turner of Philadelphia converted a basket with 8.7 left in the first overtime to necessitate a second extra frame.