Bennacer scored a first-half winner as he hammered past Alex Meret to put Milan on course for a first Champions League semi-final since 2007, when they won the competition.
Napoli, who are 22 points ahead of Milan in Serie A but were without injured star striker Victor Osimhen for the first leg, had spells of dominance at the San Siro as they saw an effort cleared off the line in the first minute and hit the bar in the second half
But Anguissa picked up two yellow cards in the space of three minutes and 45 seconds to see red in the 74th minute to halt their momentum, although Giovanni Di Lorenzo saw an effort well saved by Mike Maignan late on.
Milan, who also hit the bar in first-half stoppage time, will take a narrow lead to Naples for the return leg on Tuesday with Luciano Spalletti’s side without both Anguissa and Min-Jae Kim for the game after the defender picked up a second-half booking.
The winner of the tie will either play Inter Milan or Benfica in the semi-finals, with Inter in control after a 2-0 first-leg win in Portugal.