Piotr Zielinski opened after just seven minutes in the Stadio San Paulo with Algerian Adam Ounas adding a stunning second from a distance in the first half before Milik's second half double.
Carlo Ancelotti's side consolidated second place and replied to Juventus who had pulled 11 points clear on Friday with a confident 1-0 win over Inter Milan.
Inter Milan, in third, lose ground on the top two, falling six points adrift of Napoli after their damaging Derby d'Italia defeat where Mario Mandzukic scored the only goal.
Ancelotti said it was important to lay the groundwork ahead of next week's trip to Anfield where Napoli need a point to advance to the Champions League knockout rounds.
"Games like today have all the ingredients of a trap, especially ahead of a Champions League game," said the former Chelsea boss who rang the changes against second from bottom Frosinone.
Italian goalkeeper Alex Meret got his first start after breaking his arm following his summer move from Udinese, with Germany midfielder Amin Younes also making his debut off the bench.
Algerian international Faouzi Ghoulam more than a year after suffering a knee injury, and provided the assists for both Milik's goals.
"I congratulate those who made their debut, these players knew how to wait and be ready," said Ancelotti. "I made the decision today to start Ghoulam on Tuesday."
The hosts got off to a lively start with Poland's Zielinski opening from an angle after seven minutes, for his third goal this season.
Ounas doubled their advantage with a searing drive five minutes before the break.
Napoli squandered chances for a third with a Milik volley deflected wide and Ghoulam sending over when alone of front of goal.
But Milik headed in the third on 68 minutes off a Ghoulam corner with the Algerian defender setting up the Polish striker's seventh goal this season five minutes from time.
'Not parking the bus'
Napoli now turn their focus to Liverpool who showed their form with Mohamed Salah scoring a hat-trick in Saturday's 4-0 Premier League win away to Bournemouth.
"Hopefully he (Salah) got them all out of his system today and will run dry next week," smiled Ancelotti.
"We can start thinking about Liverpool now, but we must try to be calm and focused.
"We are in form and some players have rested today, so we arrive in the best condition.
"It's essential to have a positive approach, to try and take the initiative, also because we don't know how to play any other way.
"We can't think of defending and that's it. We are not suited to parking the bus and this wouldn't be the right game to do that either."
Ancelotti added: "I have fond memories of Anfield, as I won the Premier League there with Chelsea.
"It's a fantastic stadium and an honour for us to play there. It has a unique atmosphere – apart from the San Paolo, of course."