German Denis cancelled out Ricky Alvarez's 16th-minute opener to ensure Inter are now five games without a win against their opponents.
Alavarez was the first to react when Rodrigo Palacio headed down Mateo Kovacic's deep cross from the right as he got the visitors off to an ideal start.
However, Denis, who scored five goals against Inter last season, proved to be a thorn in the side for Walter Mazzarri's men once more as he beat the returning Walter Samuel in the air to equalise.
The home side made three changes from Saturday's 1-0 defeat to Sampdoria, while Samuel made his first appearance of the season for Inter after recovering from injury, replacing Andrea Ranocchia in defence, and Samir Handanovic returned in goal following suspension.
Atalanta had won their last two home games and were the first to threaten through Michele Canini, who saw his close-range header cleared off the line by Fredy Guarin after nine minutes following Handanovic's inability to retain the ball from a corner.
However, Inter were ahead through Alvarez seven minutes later, courtesy of a neat, swivelled finish as he latched onto Palacio’s knock-down to fire his third goal of the season past Andrea Consigli.
It was played at a frenetic pace thereafter, with Atalanta having the best of the possession despite not threatening Handanovic's goal any further.
Inter hit back through Alvarez, when he shimmied well inside the area, before shooting straight at Consigli as both sides pressed for the winner.
Yepes' fierce drive was saved by Carrizo eight minutes from time while Inter saw a penalty turned down a minute later when substitute Mauro Icardi went down in a tumble with Guglielmo Stendardo as the spoils were shared.
