It has been a disappointing first season in charge for Andrea Pirlo, with the Bianconeri knocked out of the Champions League at the last-16 stage by Porto and their hopes of qualifying for next season's competition hanging by a thread ahead of the final round of Serie A fixtures this weekend.
And they looked set for more despair when Ruslan Malinovskiy cancelled out Dejan Kulusevski's fine strike before half-time.
Juve stormed back in the second half, though, and sealed victory in their 20th Coppa Italia final thanks to Chiesa's composed finish with 17 minutes remaining.
Atalanta did most of the pressing in the early stages, with Duvan Zapata and Remo Freuler both flashing efforts narrowly wide of Gianluigi Buffon's goal.
It was Juve which went ahead, though, Kulusevski superbly whipping past Pierluigi Gollini after being picked out on the right-hand side of the penalty area by Weston McKennie.
Gian Piero Gasperini's side deservedly pulled level four minutes before the interval when Malinovskiy collected Hans Hateboer's pass and lashed a powerful strike past Buffon from just inside the area.
Gollini got down well shortly before the hour mark to paw away Kulusevski's near-post flick, while Chiesa curled against the post after a slick with involving Cristiano Ronaldo.
Chiesa was not to be denied in the 73rd minute, collecting Kulusevski's pass and then sliding home his 13th goal in all competitions this season.
Atalanta battled in the closing stages, but they never really came close to finding a goal that would have forced extra time, with Juve holding on to consign last season’s final defeat to Napoli to history.