The Thursday incident, which brought Clarkson and Pistons forward Holland technical fouls and ejections and a technical foul for Reed, came with 97 seconds remaining in the third quarter of Utah's 126-119 victory at Detroit.
Clarkson was fined $35,000 for escalating an on-court altercation and throwing his headband into the stands after being ejected.
Holland was fined $25,000 for escalating the scuffle while Pistons center Reed, was fined $15,000 for initiating the altercation.
Clarkson, an American of Filipino heritage, has averaged 15.1 points, 3.8 assists and 3.3 rebounds a game for the Jazz, who are 14th in the Western Conference at 6-20.
Holland, a 19-year-old rookie taken fifth in this year's NBA Draft, averages 6.3 points and 3.1 rebounds a game while Reed averages 5.4 points and 2.4 rebounds for the Pistons, who at 11-17 are 11th in the Eastern Conference.