Mutti, who replaced Devis Mangia just before Christmas, watched on as his side slumped to an uncontested defeat as Napoli joined Roma in sixth place, 10 points adrift of the Serie A summit.
Goran Pandev gave Walter Mazzarri's side the lead 10 minutes before the interval and Edinson Cavani made it two 10 minutes after the break.
Marek Hamsik sealed the win on the hour mark with Napoli then controlling the game with ease as the stadium emptied prematurely as the home fans voted with their feet, most of them missing Fabrizio Miccoli's 89th-minute consolation.
Cavani missed a hat-trick of chances in the first 15 minutes against his former club, getting closer and closer with a succession of headers.
Miccoli did just the same at the other end with a header which he should have got on target from seven yards.
Pandev opened the scoring as Napoli started to increase the pressure. He accepted Walter Gargano's low cross from the right and turned to slide it inside the near post from close range.
Pandev scooped another good chance over the crossbar in the 41st minute as Napoli continued to press.
Cavani made it two in the 54th minute with a fine curling effort from 25 yards which even drew respectful applause from the home fans, who have not forgotten what he achieved for them prior to his move to Napoli 18 months ago.
Pandev hit the post moments before Hamsik made it three as he skipped past the Palermo goalkeeper before tucking the ball in from a tight angle.
Napoli appeared to call it a day and just maintain possession rather than attacking and they conceded a goal when Miccoli looped his header over Morgan De Sanctis for some personal joy at the death.