Napoli's win, at one of the most difficult venues where third-placed Inter Milan were thumped 4-1 three weeks' ago, cut leaders Juventus's advantage back to eight points.
A typically flowing Napoli move began with Allan playing a long crossfield ball to Mario Rui, who drove a low, powerful ball behind the defence to Milik in the area.
The Pole, who had replaced Dries Mertens, flicked the ball up with his first touch and then volleyed past goalkeeper Etrit Berisha with five minutes left.
It was Milik's fifth league goal of the season, although the 24-year-old has only started seven of Napoli's 14 games.
"Milik has had a difficult time because he has not played regularly. He deserved an evening like this," said Napoli coach Carlo Ancelotti.
Napoli, held 0-0 at home by bottom club Chievo in their previous game, took a second-minute lead when Fabian Ruiz turned in Lorenzo Insigne's cross.
Atalanta came roaring back and equalised in the 56th minute when Duvan Zapata scored against his old club, blasting his shot past fellow Colombian David Ospina from close range.
Napoli's final pass often let them down as they enjoyed the better of the last half hour.
"It was an important response from the players," said Ancelotti, who has returned to Italian football after a nine-year absence. "You cannot always play spectacular football. Bergamo is always a difficult trip."
"They were very aggressive and forced us to play a game which was different to the one we had prepared."
Juve, chasing an eighth successive title, have 40 points from a possible 42 after their 3-0 win at Fiorentina on Saturday, with Napoli on 32 and Inter Milan on 29.
Juventus host Inter in their next game on Friday.
(Writing by Brian Homewood; editing by Ken Ferris)
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