Simone Pepe headed Juve in front in the first half before Alessandro Matri and Claudio Marchisio each scored their fifth goal of the season to keep Juventus unbeaten after their first 10 games of the season.
Sixth-placed Palermo have a 100 percent home record but have taken only one point in six away games and have yet to score on the road.
Antonio Conte's team went level on 22 points with Lazio, who have played a game more and drew 0-0 at Napoli on Saturday.
"It was a treacherous game on paper and that's how it turned out on the field. If we hadn't been on our toes, we could have been surprised," said Conte.
His opposite number Devis Mangia was baffled by his team's poor away form.
"Perhaps we need to go for a psychoanalysis to cure these problems we are suffering when we travel," he told reporters.
It was Giovinco's seventh goal of the season.
Gaetano D'Agostino and Alessandro Gazzi replied for Atalanta who twice came from behind in a battle of two promoted teams.
Chievo Verona won 2-1 at Catania and Miguel Veloso's 86th minute gave Genoa a 1-0 win over Novara, even though the hosts played the second half with 10 men after Luca Antonelli was sent off for a professional foul.
Juventus, playing their first game for three weeks, went ahead in the 20th minute when Pepe was left unchallenged to head in from Giorgio Chiellini's cross.
