The young goal machine marked his 15th of the league season to prove the difference against the hosts, who were reduced to 10 men and lie just four points above the drop zone
Stephan El Shaarawy was the hero for the visitors as he notched the only goal of the game 29 minutes in, while Atalanta slump to a defeat that leaves them nervously looking at the relegation zone down below.
Needing three points to keep up their quest for a place in the Champions League for the coming campaign, Milan nevertheless found it difficult to break down their hosts in an opening half-hour that was hectic but lacking in clear chances.
Atalanta were the first team to threaten on goal, German Denis forcing a save from Christian Abbiati as he fired in an effort from out wide that was comfortably claimed by the keeper.
With Milan imposing themselves in the middle while wasteful in their approach play, the onus once more fell on top scorer Stephan El Shaarawy to lead his side's attack. The young forward did brilliantly to twist his way to the byline, and an improvised chip with the outside of the boot momentarily had Andrea Consigli scrambling before flying just wide of the post.
The Rossoneri finally took the lead just before 30 minutes had been played, and there was little surprise over the identity of the goalscorer.
M'Baye Niang opened up the Atalanta backline with a wonderful through-ball, and El Shaarawy reacted instantly to square up to Consigli and rifle into the bottom corner for his 15th Serie A strike of the season.
The goal left only Edinson Cavani ahead of the 20-year-old as the season's most prolific marksman, and Milan took advantage to establish a strong control of the match as Atalanta floundered in their attempts to level.
A header from Cristian Raimondi steered straight at Christian Abbiati was the closest the home team came to equalising in the first half, as Milan looked comfortable spraying the ball across the pitch while the opening period came to a close.
The visitors began after the interval by exerting exactly the same dominance they had showed beforehand, pinning back their rivals in their own half as they probed for a second goal.
Atalanta were resolute, but Giampaolo Pazzini came close to a spectacular strike when his scissor-kick flew wide of the goal less than 10 minutes into the half. La Dea's plight became even worse, when Davide Brivio was expelled for a second bookable offence following a brutal challenge on Pazzini.
With Denis withdrawn to make way for defender Carlos Matheu, Milan once more lowered the tempo and looked supremely comfortable in the absence of forward threat from their opponents.
There remained the occasional charge on goal - Mathieu Flamini let loose with a stinging shot that was deflected just over - but the Rossoneri otherwise looked content to play out the remaining minutes and goad Atalanta into pushing forward, subsequently punishing them on the break.
The best action in the final moments proved to be off the ball in an increasingly bad-tempered fixture, but a spate of bookings had no effect on the score as Milan coasted to a narrow yet straightforward win.
The Rossoneri have now won six of their last eight Serie A outings, and a Champions League place that once looked out of their reach now becomes a real possibility for the Italian giants.