Ruslan Malinovskyi and Alejandro “Papu” Gomez scored in the second half after former Atalanta midfielder Dejan Kulusevski had given Parma the lead.
Immobile scored from the spot on 69 minutes and less than 60 seconds later set up Joaquin Correa for the second, before capping the comeback two minutes into injury time with his ninth goal in eight league games this term.
Coppa Italia: Atalanta reach first competition final since 1996 with victory over six-time winners Fiorentina
Atalanta reached their first Coppa Italia final since 1996 as Josip Ilicic and Alejandro Gomez scored in a 2-1 victory over six-time winners Fiorentina on Thursday
Serie A: Juventus edge second-placed Napoli in ill-tempered clash to extend lead to a mammoth 16 points
Juventus closed all talk of a challenge to their Serie A dominance after coming through a second-half onslaught at Napoli to win 2-1 in an engrossing match that saw each side have a man sent off and stretch their lead at the top to a huge 16 points.
Italian Cup: Gianluigi Buffon marks return from injury with a penalty save to help Juventus win first leg of semi-final
"I'm happy for Gigi (Buffon), who hadn't played in the Italian Cup for five years," Massimiliano Allegri added. "He hasn't forgotten everything he knew just for being out of action for 45 days.
"I need to ask myself the question what I did wrong,” Koeman added.
Wins take Napoli alongside Juventus, Inter Milan, AC Milan and Sampdoria on the top of the table. Paulo Dybala's hat-trick help Turin giants lead the table on goal difference.