Italy forward Chiesa, on loan at Juve from Fiorentina, fired home into the bottom corner in the 73rd minute after Ruslan Malinovskyi had cancelled out Dejan Kulusevski’s first-half opener for Juve.
Andrea Pirlo’s side, who have conceded the Serie A title for the first time in 10 years this season, lifted the trophy for a record-extending 14th time.
Atalanta, who finished the game with 10 men after Rafael Toloi was shown a straight red card in the 88th minute for dissent, lost in the final for the second time in three years.
They were beaten 2-0 by Lazio in the 2019 final and last won the cup in 1963.
As for PSG, Argentina striker Mauro Icardi took advantage of a defensive slip to guide the ball home following Kylian Mbappe’s pass in the 19th minute.
PSG looked the more likely to extend their lead and Mbappe put the icing on the cake with a sublime chipped finish nine minutes from time to seal the club’s 14th Coupe de France win.
Additional reporting by PA.