Edin Dzeko's fine strike just before half-time had given the Giallorossi the advantage at the Gewiss Arena - but finishes from Jose Luis Palomino and substitute Mario Pasalic turned things around before the hour-mark.
Atalanta then saw out the game; extending their lead in the race for the Champions League places to six points.
The Giallorossi are back in action on Thursday, as they host Gent in the first leg of their Europa League last-32 clash at the Stadio Olimpico.
Paulo Fonseca's side are then back in Serie A action on Sunday, as Lecce come to the capital.
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