Luca Pellegrini was the first to receive a second booking for fouling Christian Pulisic.
Ivan Provedel made two saves before AC Milan’s Noah Okafor scored from 16 yards out in the 88th minute to seal the victory.
In added time, two Lazio players received straight red cards: Matteo Guendouzi for shoving over Pulisic, and Adam Marusic for reacting angrily to the referee.
After former Chelsea forward Pulisic fouled Guendouzi, the American was sent to the ground in a fit of rage, leaving the hosts down to eight men for the last few minutes.
In a heated match, three Lazio players received yellow cards and six Milan players were booked.
