Cleveland was trailing 78-76 with 18.1 seconds left in regulation when they went on a fast break and Irving twisted around Nick Calathes to bank in a score-tying shot while falling to the floor.
Luol Deng began the overtime with a 3-pointer and the Cavs went on to claim a second straight win.
Dion Waiters scored 18 points and Anderson Varejao pitched in with 14 rebounds and five assists.
Calathes led the Grizzlies with 17 points, six assists and five rebounds.
James Johnson popped in 15 points off the bench as Memphis fell for the third time in four games.