Dani Alves appeared to have won the game for Juventus when he headed them in front in the 83rd minute but Remo Freuler pounced to equalise six minutes later as he punished some sloppy defending.
Juventus, who moved nine points clear of AS Roma, have one of the strongest defences in Europe and have conceded only 22 goals in the league all season in 34 games.
Juventus coach Massimiliano Allegri was more angry at his team for pouring forward to try to grab a late winner than for the earlier mistakes they made.
"We conceded two goals after making mistakes, the sort of mistakes which shouldn't happen but the lads are human," he said. "The important thing is to stay calm."
"Once it was 2-2, we charged forward looking for the third and we risked throwing everything away. Points (not just wins) are important as well."
Fifth-placed Atalanta have been one of the surprise packages in Serie A this season, losing only three times at the Atleti Azzurri d'Italia stadium, and they gave Juve a hard time as expected.
Juventus twice escaped after mistakes by defender Giorgio Chiellini set up the hosts but there was no let-off when Andrea Conti forced Alejandro Gomez's cross over the line on the stroke of halftime.
The Turin side equalised six minutes after halftime when Miralem Pjanic's free kick flew across the face of the goal and was turned into his own net by Leonardo Spinazzola at the far post.
Atalanta goalkeeper Etrit Berisha twice denied Sami Khedira with excellent saves before Alves got in front of his marker to meet Pjanic's long ball at the far post with a diving header and give Juventus the lead.
Juve's usually impregnable defence let them down when Pjanic and Stephan Lichtsteiner collided while trying to clear and the ball ran loose to Freuler.
His first shot was blocked by Gianluigi Buffon but the Swiss forced home the rebound despite the attention of three defenders who were left slumped on the ground.
(Writing by Brian Homewood in Berne; Editing by Clare Fallon)
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