NBA bans Utah's Dunn for two games and Houston's Smith one
The altercation took place five seconds into the second quarter of Houston's 147-119 home victory over Utah on Saturday.
Dunn was suspended for initiating an altercation and throwing a punch at Smith, who received a one-game fighting ban.
Both players were issued technical fouls and ejected from the game.
Dunn, a 30-year-old American in his eighth NBA season, will start his suspension on Monday when the Jazz play host to Dallas and also miss Wednesday's home game against San Antonio.
Smith Jr., the 20-year-old son of a former forward who played five NBA seasons, will serve his suspension on Monday when the Rockets will host Portland.
Smith is averaging 13.3 points and 8.5 rebounds a game for Houston, which at 35-35 is 1.5 games behind Golden State for the final Western Conference play-in spot.
Dunn is averaging 5.3 points, 3.9 assists and 2.8 rebounds a game for the Jazz, who at 29-42 are eight games behind 10th-place Golden State.