Robinho had a great chance to give the hosts an early lead, but after being picked out unmarked at the back post, he side-footed a volley wide.
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They came even closer soon after when Robinho played a low delivery into the box that was met by Bryan Cristante, but he saw his attempt come back off the bar.
Kaka was next to test the keeper as he fired in a low strike from the edge of the box, which Consigli stretched out a hand to tip wide.
The Brazilian did not have to wait long for his next chance and finally broke the deadlock with his 100th goal for the club.
Urby Emanuelson played the ball through to Kaka, who took a touch before slotting a low strike past the keeper and into the bottom corner of the net.
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In the final minute of the first half Atalanta came close to snatching an equaliser when Cristian Raimondi fired a strike from outside the box that came crashing off the post.
Milan doubled their lead in the 65th minute of the match when Mario Balotelli drilled in a low cross that hit Robinho and landed kindly in front of Kaka to slot in from close range.
Two minutes later they scored their third goal of the afternoon through Cristante, who picked up the ball 25 yards out from goal before firing a low strike into the bottom corner.
Balotelli came close to adding a fourth goal for the home side after picking up the ball in midfield and driving into the box, before seeing his low strike saved by the legs of the keeper.
Consigli was called into action again minutes later and denied Kaka his hat-trick by pushing the Brazilian's fierce long-range effort wide.