The dustup occurred with about 10:47 remaining in the first half Wednesday at TD Garden. The Celtics won the bout 96-83, taking a 3-2 lead in the series.
Morris tipped the pass away from Nance as the Cavaliers forward fell out of bounds. Morris then looked down at Nance on the baseline after making the play. Nance got up and pushed Morris in the back after the taunt. Morris shoved Nance back, hitting him in the side of the face.
A hoard of Celtics surrounded the players before wrapping up Morris and keeping him away from Nance. Technical fouls were then assessed to Morris, Nance and Terry Rozier.
The crowd at TD Garden saluted Morris with an applause. He winked back at Nance after the altercation.
Morris was asked after the game about what he said to Nance.
"I can't say that on camera. I definitely can't say it on camera," Morris told reporters. "But it must've gotten to him because he got up and he did his little whatever you want to call it."
Nance finished the game with two points, six rebounds, four blocks and two assists. Morris had 13 points and six rebounds. Rozier had eight points, six assists, six rebounds and three steals for the Celtics.
Game 6 of the series tips off at 8:30 p.m. Friday at Quicken Loans Arena in Cleveland.