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Pablo Barrientos came close for the visitors early on, but saw his low strike from the edge of the box pushed wide by the keeper.
Atalanta took the lead in the 67th minute of the match when Cristiano Biraghi gave away a penalty and Denis stepped up to score from the spot.
Maximiliano Moralez scored their second goal of the game after he drove into the box and fired past the keeper.
Catania pulled a goal back when Sebastian Leto latched onto a pass from Kingsley Boateng and slotted the ball into the net, but they could not find a second goal and Atalanta held on to claim the three points.