Irving scored 39 points and his layup miss was tipped in by Tristan Thompson with two seconds to go in the fourth period, creating a 96-96 tie.
Cleveland improved its home record to 8-4 and handed the lowly Bucks their fifth straight loss. Milwaukee has an NBA-low five wins.
Irving's two free throws with 22 seconds left in overtime put the Cavaliers in front by four, but O.J. Mayo hit a 3-pointer for the Bucks to cut their deficit to one.
Irving again made two foul shots with 10 seconds left and Mayo once more was called on to attempt a long-range shot in hopes of creating a second overtime. This time Mayo missed an open try, leaving him with a team-high 20 points.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys