The home side took an early lead thanks to Tommy Maistrello who first-time volleyed home a cross from Alessio Vita in the 3rd minute.
Cittadella doubled their advantage 20 minutes later with Mirko Antonucci sending the keeper the wrong way from the penalty spot.
Palermo halved the deficit in the 33rd minute with a spot kick of their own, rocketed into the top left corner by Francesco Di Mariano.
The away side equalised in first half stoppage time thanks to an acrobatic overhead shot by Matteo Brunori.
Palermo then went ahead in the 64th minute with Di Mariano bagging a brace.
The midfielder side footed home a square ball from Edoardo Soleri that went all the way across goal.
The miracle comeback wasn’t to be, however, with Maistrello also scoring a double just ten minutes later.
His header from Federico Giraudo’s cross was too powerful for Palermo goalkeeper Mirko Pigliacelli, who got a hand to the ball but was unable to keep it out.
Simone Branca was sent off five minutes from time, leaving Cittadella to hold out with ten men.
Cittadella are five points clear of the relegation playoff zone, while Palermo out just outside the top eight.
