The contest was deadlocked at 83-83 with less than 5 minutes to play when Irving went on his tear, hitting a jumper, a 3-pointer and two layups while the Hornets were going without a point.
Cleveland ended a three-game losing streak.
Irving wound up with 35 points, five rebounds and seven assists. Dion Waiters added 16 points and C.J. Miles had 11.
New Orleans placed six players in double figures, led by Brian Roberts' 17.