The dispute was a blast from the past on a night in which the Cavs never trailed and led by as many as 28 points in a 117-104, Game 1 win.
It brought to mind the Cavs and Celtics' first-round playoff series in 2015 that devolved into a physical affair with Kelly Olynyk wrenching Kevin Love's shoulder out of its socket, JR Smith drawing a two-game suspension for his flagrant foul on Jae Crowder that caused Crowder to fall to the floor and sprain his left ACL and Kendrick Perkins scuffling with Crowder.
However, Thompson vows there has been no carryover effect as the Eastern Conference finals continue.
"Whatever happened in the past is in the past," Thompson told ESPN after finishing with a career-playoff-high 20 points on 7-for-7 shooting, nine rebounds and two steals. "We got guys that understand that whenever you take extracurricular actions, there's consequences for it and for us. We need everyone, every game. So I'm not going to put myself in the position to hurt my team or my teammates."
Thompson and Smart were called for a double foul with 3:10 remaining in the third when the Cavs big man threw the Boston guard's arm off him as the two got tangled up while fighting for rebounding position.
Smart, who left the arena without speaking to reporters, took exception to Thompson's aggression. Thompson then took exception to Smart elbowing him, and the two went chest to chest, prompting the referee to blow the whistle.
A couple minutes later, Thompson and Smart collided once again, with Thompson being called for a foul with 1:44 remaining in the third for running over Smart and causing him to fall to the floor.
"I just boxed out, and he's crafty," Thompson told ESPN. "I just got to move out of the way and get back on D."
Smart eventually fouled out, finishing with 6 points, 3 rebounds, 3 assists and 2 steals in 21 minutes.
Thompson said there was nothing personal between him and Smart that was behind the flap.
"No history," Thompson told ESPN. "He wasn't at Oklahoma State when I was at Texas. He's younger. But he plays hard. He plays hard. He does the same thing I do. He's a guard that plays hard, and you got to respect it. He leaves it all on the line, and he kind of gives them that boost."
Smith told reporters he expects more physicality from the Celtics in Game 2.
"For them to come out swinging, playing scrappy like they do," Smith said, "they've been playing like that all year. Whenever their backs are up against the wall, they tend to play better, just like we do. We just got to expect that and understand there might be dirty plays, might be cheap shots coming from the other side just because they are fighting for their lives at this point. We just got to keep doing what we've been doing."
The Cavs, 9-0 this postseason with a potential Finals three-peat against the Golden State Warriors looming on the horizon, are aware that responding to any "dirty plays" from the Celtics with flagrant action of their own could affect their chances of repeating.
Thompson said the Cavs are above that.
"I'm not going to do that," Thompson told ESPN. "We're on a mission. I'm not about to let a player take me out of my element and force me to do something very AAU-ish by retaliating. Save that for the AAU games."