Hernanes was the star of the show scoring twice in either half while he also set up Miroslav Klose for his strike as Vladimir Petkovic's side registered their third league win in a row.
Walter Mazzarri's men are well fancied to mount a serious title challenge this campaign and have backed that up so far, winning all three of their games.
They were in control from the moment Edinson Cavani netted a third-minute penalty and, with Goran Pandev and Lorenzo Insigne also on target, Marco Parolo's strike was rendered worthless.
Bologna came from two goals down to claim their first points of the season with a 3-2 victory over shellshocked Roma at the Stadio Olimpico.
The Giallorossi looked to be cruising when Alessandro Florenzi and Erik Lamella struck in the first 15 minutes, but two goals in as many second-half minutes from Alberto Gilardino and Alessandro Diamanti brought Bologna back on level terms.
And there was one final twist in the dying seconds when Gilardino grabbed his second of the match after an embarrassing mix-up in the Roma defence.
The Uruguayan scored five minutes before half-time to give Palermo the lead, but Sau's reply two minutes from the end meant both sides failed to get the win they were looking for.
The 1-1 draw leaves both island clubs still searching for their first wins of the season.