Ismael Bennacer scored shortly before the end of a first half that Napoli had dominated for long stretches.
Both teams also hit the crossbar before the visitor's midfielder Andre-Frank Zambo Anguissa was sent off 16 minutes from time.
Milan routed runaway Serie A leaders Napoli 4-0 when the two teams met on April 2, and the visitors were missing leading goalscorer Victor Osimhen and Giovanni Simeone through injury at the San Siro in their first ever quarter-finals appearance.
Nevertheless, Napoli got off to an aggressive start and had four clearcut opportunities in as many minutes.
The hosts broke the deadlock five minutes from halftime as Brahim Diaz sped forward from midfield and laid the ball off to Rafael Leao. His attempt at a one-two didn't quite come off but it came through to Bennacer to fire into the top corner.
Napoli's chances of getting back into the match diminished when Anguissa was shown a second yellow card for a high tackle on Theo Hernandez four minutes after being booked for a foul on the same Milan defender.
"We're halfway up the mountain but normally the last few bends are the hardest to overcome," Milan coach Stefano Pioli said.
"A hard match awaits us in Naples … none of us think we're already through."
AAP
