A stunning strike from Federico Chiesa put the Italian champions in front in the first half, but Remo Freuler's powerful effort crashed off the bar and in to earn the visitors a deserved point after the break.
Ronaldo spurned a golden chance to put the hosts back in front minutes later, but his tame spot kick was comfortably held by the impressive Pierluigi Gollini.
Pirlo's side are third with 24 points, six ahead of Atalanta in eighth, and although they remain unbeaten this season, they have drawn half of their 12 league games.
"You need to take bring the result home in these games," Juventus coach Andrea Pirlo said to Sky Italia.
"We had a lot of chances but didn't manage to close it out, when you leave the game in the balance anything can happen."
Alvaro Morata was guilty of an extraordinary miss early on, when the Juve striker latched onto a loose ball six yards in front of an open goal and back-heeled a limp finish harmlessly wide.
Both goalkeepers were decisive, with Gollini making two superb sprawling saves from Morata shots in the second half and Juve's Wojciech Szczesny denying dangerous efforts from Duvan Zapata, Cristian Romero and substitute Alejandro Gomez.
"Gollini was amazing," said Atalanta coach Gian Piero Gasperini.
"He saved a penalty on Ronaldo, who misses one in a hundred. We're happy for him, a bit less for Szczesny who made a great save on Romero, I thought it was a goal."
Speculation over the potential departure of Atalanta captain Gomez following reports of a fall-out with Gasperini overshadowed the visitors' build-up to the game, as the Argentine was left out of Sunday's win over Fiorentina and on the bench in Turin.
But the playmaker made an instant impact after being introduced early in the second half, pulling the strings to help his team draw level and create several good chances while he was on the pitch.