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start with the Rossoneri to by making it six goals in his past four matches and, although the 23-year-old was later withdrawn following a knock to his foot, Gennaro Gattuso's side were able to sew up a crucial result in the fight for Champions League qualification.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.
What's next?
Milan host relegation-threatened Empoli in their next Serie A fixture on Friday, while Atalanta visit Torino the following day.
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