On target in each of his previous three appearances, Poland international Piatek struck either side of half-time to help secure a come-from-behind victory that moved Milan four points clear of the hosts, who slipped down to seventh.
His first cancelled out Remo Freuler's 33rd-minute opener before Hakan Calhanoglu completed the quickfire turnaround with a thunderous drive 10 minutes after the interval.
That set the stage for Piatek to extend his prolific start with the Rossoneri to by making it six goals in his past four matches and, although the 23-year-old was later withdrawn following a knock to his foot, Gennaro Gattuso's side were able to sew up a crucial result in the fight for Champions League qualification.
Franck Kessie, facing his parent club, fluffed two good chances to open the scoring in the early stages, blasting a shot wastefully high and nodding a Suso cross wide of the near post.
Atalanta were otherwise on top during the first half and deservedly led when Freuler forced a first-time effort through Gianluigi Donnarumma following Josip Ilicic's fine build-up play.
Piatek, though, ensured parity was restored on the stroke of half-time with a sublime flicked finish across Etrit Berisha from Ricardo Rodriguez's cross.
Atalanta looked to be reasserting control until, out of nothing, playmaker Calhanoglu rifled an unstoppable bullet into the bottom-right corner.
The visitors were buoyed and Piatek put the seal on their impressive fightback by bravely rising between goalkeeper Berisha and Duvan Zapata to head in Calhanoglu's corner, stretching Milan's unbeaten streak to seven Serie A matches.
What does it mean? Rossoneri on course for fourth
There is a still a long way to go, but this result puts Milan in a strong position in what is a tightly contested race for fourth spot.
Roma and Lazio will have opportunities to close back to within a point over the next couple of days yet, with a commendable maturity and a striker in irresistible form, Gattuso's side appear well placed to return to Europe's top table.
Piatek the catalyst
Comparisons have been made to Andriy Shevchenko and Piatek is doing nothing to play down the hype surrounding his flying start at Milan.
He displayed sublime movement and a silky touch for his first goal, with sheer determination then on show as he made it a double after half-time.
Gattuso will hope the kick he sustained in the second half is not serious.
Zapata outshone at home
Atalanta striker Zapata is rivalling Piatek for the golden boot but the Colombia centre-forward was unable to match his opposite number's efforts in Bergamo.
The 27-year-old struggled to make an impression in attack and failed to adequately challenge Piatek in the air for the Milan man's second goal.
Key Opta facts
42 - In all their previous 13 campaigns in the three points for a win era, AC #Milan have always finished in the Top-4 of the table when they managed at least 42 points after 24 MDs. Aim.#SerieATIM #AtalantaMilan pic.twitter.com/keckCJrQrP— OptaPaolo (@OptaPaolo) February 16, 2019
- Milan have gained 13 points from losing situations, the joint-most in Serie A this season (level with Juventus).
- Atalanta have scored in each of their last 16 Serie A games, their longest streak since January 2007.
- Milan scored three goals with only three shots on target in the match.
- Before Piatek, the last AC Milan player to score in each of his first three Serie A starts with the Rossoneri was Mario Balotelli (February 2013).
- Piatek has scored a goal every 60 minutes on average with AC Milan – he had a goal every 123 minutes with Genoa.