A goal in each half helped the Serie A champions get over their draw to Sassuolo last weekend and the midweek defeat to Olympiakos in the Champions League
Massimiliano Allegri's side suffered a second successive Champions League defeat against Olympiakos in midweek, and Roma drew level with them at the summit of the Italian top flight with a draw at Sampdoria on Saturday.
But goals in each half from Arturo Vidal and Fernando Llorente gave Juve a comfortable home win on Sunday - a victory that puts them three points clear of Rudi Garcia's men.
The champions appeared cagey early on, but were settled by Vidal's deserved 32nd-minute opener, before Llorente sealed a 23rd straight Serie A home win with his first goal of the season shortly after the hour.
Palermo, by contrast, remian in the bottom three with just one win from their eight matches since returning to the top flight.
Allegri made three changes to the Juve side beaten in Athens on Wednesday and, after a cautious opening to the game, it was one of those introduced - Claudio Marchisio - who registered the first meaningful attempt.
The midfielder went close with two volleys at goal in as many minutes, the second dipping just too late after the ball fell nicely for him 15 yards out.
Juve looked more comfortable thereafter, and with the home crowd behind them, started asking questions of the visitors.
Vidal floated in between the lines and almost created the opener in the 17th minute as he picked out Llorente from the left, but the Spaniard headed straight at Stefano Sorrentino.
Juve were dominating possession, but they were reminded of Palermo's threat on the counter when Paulo Dybala and Franco Vazquez combined for the latter to force Gianluigi Buffon into action just before the half-hour mark.
That scare sparked increased focus from Juve and they took the lead on 32 minutes after a break of their own.
Carlos Tevez led the charge, travelling forward with the ball at pace before timing his pass perfectly for the overlapping Vidal to slot coolly beyond Sorrentino with his left foot.
The tension that had inhibited the hosts' play disappeared after the opener. Vidal should have doubled the lead 11 minutes after half-time when Zouhair Feddal mindlessly teed him up six yards from goal, but the Chilean blazed over the bar.
Tevez continued to cause Palermo problems and Sinisa Andelkovic almost turned the striker's dangerous cross into his own net on 64 minutes.
There was no doubt from the resulting corner, however.
Llorente rose highest in the box to meet Andrea Pirlo's out-swinging cross and direct low out of Sorrentino's reach.
Juve substitute Sebastian Giovinco almost got in on the act late on, as first his powerful shot from a tight angle was well saved by Sorrentino's feet before the 27-year-old hit the post from 18 yards.
But the hosts' easy victory had long been secured, as they went some way to getting over their continental heartache.