The Rosaneri took the lead in the fifth minute through Mauro Formica and it was a one-sided opening 45 minutes in which Palermo failed only to add a second goal.
Chievo responded well in the second half and found an equaliser through Cyril Thereau's penalty, but they were unable to find a winner despite creating the better chances.
For his second game in charge of the Sicilians, Alberto Malesani took a gamble by leaving Fabrizio Miccoli and Paulo Dybala on the bench, instead choosing Mauro Boselli and Formica.
It was a choice which the former Bologna and Genoa coach would not regret either as Formica repaid his faith just five minutes in.
Francesco Acerbi made a hash of his attempted headed clearance and the ball fell kindly to Formica, who shot on the turn past Christian Puggioni.
The goal gave Palermo an ideal start, but they were unable to build on it, even though Chievo showed little going forwards, failing to test their former goalkeeper Stefano Sorrentino even once in the first half.
Sorrentino was called into action five minutes into the second half to keep out Sergio Pellissier's deflected shot, and five minutes later, he was faced with Thereau from the penalty spot after Santiago Garcia handled the ball in the area.
Thereau made sure Sorrentino did not get close to his spot kick as he brought the Flying Donkeys level.
The game sparked Chievo into life and Thereau tried to put them in front with a direct free-kick and then a volley, but he missed the target both times.
Miccoli was sent on by Malesani as the final throw of the dice, but when his free-kick hit the wall rather than finding the target, it became clear it was not going to be their day.
They held on for a point, though, to move off the foot of the table, a point clear of Siena.