After Romelu Lukaku converted a penalty in added time to level for Inter on Tuesday, the Belgium striker picked up his second yellow card for apparently taunting the Allianz Stadium crowd.
Juan Cuadrado, who had put Juventus ahead in the 83rd minute, and Inter goalkeeper Samir Handanovic were also sent off as they clashed after the final whistle.
Players from both teams then got involved as they tried to separate the two.
“It's nothing, just a bit of chaos at the end of a balanced game,” Juventus coach Massimiliano Allegri said.
“We knew it would be difficult. Although they were coming off a difficult period, they are still Inter and proved it tonight.”
Lukaku, Cuadrado and Handanovic should all miss the second leg on April 26.
The result didn't do much to alleviate the crisis at Inter, who have lost three straight Serie A matches.
The outcome of the semi-final and Inter's upcoming Champions League quarter-final against Benfica could be crucial in determining whether Simone Inzaghi stays on as Inter's coach.
Inter beat Juventus 4-2 after extra time in last year's final to win their eighth Italian Cup but Juventus has had the upper hand this season, beating Inter twice in Serie A — including a 1-0 victory little more than two weeks ago.
While both teams had a few close chances, the match appeared headed for a 0-0 draw until Colombian Cuadrado was left virtually unmarked to score with a long range shot in the 83rd minute.
Juventus defender Gleison Bremer was penalised for a handball to set up Inter's penalty, after which Lukaku held his finger to his lips as if to silence the crowd.
Last-placed Serie A club Cremonese host Fiorentina in the other semi on Wednesday.
AAP
