The Nerazzurri targeted the first breakthrough and it nearly came on the half-hour mark when a side-footed effort from Romelu Lukaku came off the woodwork.
Napoli weren't overawed by the table-topping side and demonstrated such nine minutes from halftime after a cross from Lorenzo Insigne forced goalkeeper Samir Handanovic to an own-goal.
Although the lead was nearly short-lived a minute later as a floating ball from a free-kick by Christian Eriksen saw Lukaku struck the base of the post with a close-range shot.
Inter returned for the second half renewed and subsequently drew level five minutes in from a first-time strike from outside the area by Eriksen.
However, the host nearly restored the lead from an effort at the back post by Fabian Ruiz following an in-swinging free-kick later on but the Spaniard dragged past the near corner.
Inter decided to add fresh faces from the dugout inside the final stages of the match and hauled off Matteo Darmian in place of Croatian international Ivan Perisic.
Antonio Conte's men struggled to contain the host a little later when a shot from close-range by Matteo Politano rattled the crossbar.
Further promising attempts from either side followed right inside the final whistle, but it finished 1-1 in the end.
Bianconeri were without Cristiano Ronaldo due to a muscle injury and Paulo Dybala was recalled in his place to partner Alvaro Morata upfront alongside the return of Alex Sandro and Weston McKennie.
After a slow start, Matteo Pessina had a glorious chance for the Black and Blues in the 24th minute after exchanging passes with Luis Muriel to go clear on goal inside the box but he hesitated before a he unleashed a strike that took a deflection off Matthijs De Ligt.
Morata also had a big chance for Juventus ten minutes before the break with a chipped effort over goalkeeper Pierluigi Gollini from close range that was cleared off the line by Berat Djimsiti after Chiesa won possession off Joakim Maehle at the near post.
The sides were yet to find their rhythm early in the second stanza and Andrea Pirlo was forced to make a change just before the hour-mark after Chiesa got injured and he brought on Danilo in his place, in what became a tactical move.
Muriel came very close to breaking the deadlock for Atalanta a moment later after a powerful curling strike from the edge of the box that missed agonisingly wide.
Ruslan Malinovskiy produced fireworks for the visitors, as firstly in the last four minutes he unleashed a strike from long range that was heroically kept out of the top corner by goalkeeper Wojciech Szczesny.
However, Malinovskiy finally snatched the winner for Gian Piero Gasperini's men in the last three minutes with a cracking strike from the edge of the box that took a deflection and wrong-footed Szczesny.
