Atalanta had a chance to open the scoring just over 10 minutes into the tie when Leonardo Blanchard brought Mauricio Pinilla down in the box, but the striker's low shot from the resulting penalty was kept out by Nicola Leali.
Atalanta did break the deadlock midway through the first half, though, when Guglielmo Stendardo fired the ball in from the edge of the box after Frosinone thought that they had cleared a corner.
Pinilla could have doubled their advantage five minutes later when Kurtic played the ball in for the striker, but his low drive was turned behind for a corner.
The hosts continued to show the greater level of urgency early in the second half, giving Pinilla a chance to add a second on the hour mark after Gomez won a free kick, but his flick-on was blocked.
The miss allowed Atalanta to get the ball back, and they doubled their advantage just four minutes later when Gomez unleashed a powerful drive from 25 yards out, blasting the ball just inside the left post.
Drame could have added a third for the hosts in the closing stage of the match, collecting a through-ball from Pinilla, but his curling finish was kept out by the post.
The result moves Atalanta up to ninth in the table, while Frosinone sit 19th, having failed to pick up a point from their opening two matches of the campaign.