The brouhaha started when Milwaukee's Malcolm Brogdon delivered a hard foul to Young with 36 seconds left in the quarter.
Young shoved Brogdon, and Monroe quickly shoved Young. Russell and Lakers rookie Brandon Ingram then both engaged with Monroe while every player on the court joined the fray.
The officials called double technical fouls on Russell and Monroe, ejecting them both. Young had a technical foul earlier in the game, and he was ejected for his second T.
Young had 16 points and Russell had 14. Monroe had 12 points for the Bucks, who took an 84-77 lead into the fourth.