Nicola Pozzi hit a double and Italy forward Antonio Cassano was on target as the visitors frustrated the man who steered them to a fourth-place finish last term.
Goals by Claudio Marchisio, Simone Pepe and Fabio Quagliarella at least made sure Juve got their first point after they lost their opener 1-0 at Bari despite almost a whole new team of signings after last season's miserable campaign.
Juve are level with last season's runners-up AS Roma, who were thrashed 5-1 at Cagliari on Saturday, and two points behind AC Milan, who lost 2-0 at promoted Cesena with Sweden's Zlatan Ibrahimovic and Brazil's Robinho making their debuts.
"Teams don't always get things right in tactical and physical terms at the start of the season, especially when there are lots of changes (in the squad)," Juve captain Alessandro Del Piero told Rai television.
"So it is not surprising (the big teams are having problems). The so-called little teams have improved significantly."
Marchisio replied for Juve six minutes later thanks to a shot with the outside of his right foot after Milos Krasic headed on Del Piero's cross from the right.
"It was a different performance to Bari," said Del Neri. "We played excellent football in the second half. We were naive in the incidents when we conceded the goals but we'll improve."
"We have to have the right movement. With hard work and clear ideas we'll be able to stop opponents having chances. The three goals could have been avoided but we've made a step forward."
Chievo are top after Davide Moscardelli struck before halftime to wipe out Mattia Destro's early opener for Genoa before Michele Marcolini and Sergio Pellissier clinched the win in the second half.
