Goaks from Piotr Zielinski and Dries Mertens had the hosts ahead after Ruslan Malinovsky had given Atalanta a seventh minute lead with a superb shot from the edge of the box from Duvan Zapata's cutback.
After Mertens had put away a breakaway goal two minutes into the second half, Atalanta piled on the pressure again, forcing David Ospina into some good saves, and Zapata hitting the post.
But the Colombian goalkeeper could do nothing about Merih Demiral's shot on 66 minutes as the Turk blasted a shot home from close quarters to level matters.
Just five minutes later, Napoli was behind again after Remo Freuler coolly passed the ball into the net from the edge of the box, and Atalanta didn't surrender its lead, despite the hosts creating a couple more presentable chance before the final whistle.
Luciano Spalletti was keen to focus on the positives after the match, suggesting his previous Serie A leaders had "played great football".
“We were unlucky because we did play well. We lost against a very good team but we showed our quality and competitive nature despite the absences," he said.
“This group of players is doing great things and we’ll stay right up there while all our players get back to fitness.
“There are many positives to take tonight besides the result. We deserved to equalise in the last ten minutes and I think that would’ve been a fair reflection, but I do congratulate Atalanta. It was a thrilling match in which both teams performed at a high level.”