Fredy Guarin had an early sight of goal for the hosts when he was picked out on the edge of the box, but he could only place his shot wide of the post.
The midfielder came close again moments later as he worked himself some space to shoot before firing a long-range effort narrowly over the bar.
Atalanta continued to threaten and were inches away from taking the lead when Denis met Giacomo Bonaventura's cross and powered a header against the bar.
In the 35th minute Atalanta took the lead through Bonaventura, who was picked on the edge of the box before powering a low strike into the bottom corner.
Their lead didn't last long as within a minute Inter were level, when Icardi burst into the box and drilled an effort past the helpless Consigli.
Danilo D`Ambrosio had a chance to put his side ahead in the final minute of the half, but after being picked out inside the box he volleyed an effort wide of the post.