Smith took exception to what he felt was an intentional elbow from Irving after the whistle and came after the Boston Celtics' All-Star point guard with some unkind words.
Both players were assessed technical fouls for the minor dust-up.
Irving ultimately got the last laugh, finishing with 23 points on 10-of-18 shooting in a 97-90 Celtics win, while Smith shot 4-of-16 in a losing effort. Irving handily won the individual matchup, working the rookie on both the offensive and defensive ends of the floor.
Irving downplayed the incident after the game, saying he also tried to go at established point guards when he was matched up with them as a rookie.
"I've had the unique opportunity to play well against some of the best point guards, and struggle against them as well," he told reporters. "And they'll use some veteran savvy in order to take you out of your game. You have to just learn from that.
"The mix-up in the game, that's always part of it. People bumping, trying to prove something, that's always fun. And it stays within the game. You understand that, it's the competitive streak, and from that point it just becomes, 'who's going to continue to stay within the game plan?'"
Irving also said he's been tracking Smith's progression for a while.
"When I was coming up, I knew about these guys when they were in middle school and high school," he said. "I'm just an avid YouTube watcher and an avid studier of people's games, so I've been watching him since he was in middle school, before he was doing windmills on his AAU team in North Carolina. So I've been studying him for a while, and to play against him now, as a 25-year-old evolved man, is awesome."