A 1-1 draw tonight at the Stadio Diego Armando Maradona sealed progression for the Rossoneri after a 1-0 win at San Siro last week, on a dramatic evening where both sides missed from the spot.
It marks another successful evening in Naples for Milan, who won 4-0 here in the league just 16 days ago.
Luciano Spaletti's side will now have to focus purely on maintaining their big lead at the top of Serie A, to seal a first Scudetto since 1990.
Napoli were given a big boost pre-kickoff as Victor Osimhen was named among the starters for the first time since before the international break.
After making 10 changes to the side for their draw with Bologna at the weekend, Stefano Pioli named the same Milan side that beat Napoli last week in the first leg.
An impressive record of five Champions League games without conceding for Milan was put under intense pressure early on, as the visitors were under siege for the opening 20 minutes as Napoli's pressure was incessant.
However, the electric atmosphere inside the Maradona fell flat midway through the first half when referee Szymon Marciniak pointed the penalty spot down the other end, after Mario Rui wiped out Rafael Leao.
Olivier Giroud stepped up for the spot kick, but his penalty was struck at the perfect height for Alex Meret in the Napoli goal who kept it out.
The Napoli number one came to the rescue again, correcting the situation after his poor pass out from the back to deny Giroud again from close range smartly with his legs.
However, he would be helpless as Milan eventually took the lead shortly before halftime, with Giroud coming up with the opener.
All the hard work was done by Leao who ran three quarters of the pitch with the ball at his feet, leaving Giovanni Di Lorenzo, Tanguy Ndombele and Amir Rrahmani in his wake, before squaring the ball for the Frenchman who had a tap in, to put the tie almost out of reach for the hosts.
The Partenopei came out for the second half on the offensive, with Khvicha Kvaratskhelia firing over the bar just 35 seconds after the restart after some great work on the left wing.
The Georgian winger blazed over once more in a similar scenario, with substitute Hirving Lozano also guilty of firing high over the crossbar soon after.
Mathias Olivera squandered a golden opportunity just after the hour, when he was left unmarked at the back post from a corner, but got his header all wrong, missing the target.
As Milan cleared, intercepted and blocked everything that came into their penalty area, Napoli were eventually provided with an opportunity to get back into the tie, when Fikayo Tomori's stray arm blocked Di Lorenzo's cross, resulting in a penalty for the home side.
However, after an already frustrating evening for Kvaratskhelia, Napoli's revelation this season was denied by the brilliant Mike Maignan, who got down expertly to his right-hand side to turn the penalty around the post.
With Napoli throwing everything at the Milan rearguard, Osimhen proved his worth by netting a goal three minutes into stoppage time to give Milan a late scare, but the Rossoneri held on to progress 2-1 on aggregate.
With Napoli now only fighting on one front, they travel to Turin to face Juventus on Sunday in a heavyweight encounter in Serie A, as the Neapolitans look to hold onto their 14-point advantage.
Milan now have a Champions League semi-final to look forward to, most likely against bitter rivals Inter Milan, but they still need to ensure they finish in the top four this season, with a home tie against Lecce next up for Pioli's men at the weekend.