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.
Chievo Verona top the standings with six points after maintaining their perfect start with a 3-1 victory at Genoa.
Del Neri can take consolation from the misadventures of other big teams expected to mount a title challenge.
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.
Treble winners Inter Milan scraped a 2-1 home win over Udinese on Saturday and have four points.
"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."
Samp had the better of a lively opening spell and Cassano should have made more of two fine opportunities.
Pozzi, in the starting line-up after a back problem ruled out Giampaolo Pazzini, went close twice before latching on to a Cassano pass and using the ample space to fire home in the 37th.
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.
Pepe had the last say in a goalmouth scramble to put Juve in front five minutes after the break but Cassano restored parity with a diagonal shot that crawled into the net in the 64th after Marco Storari got a hand to it.
Quagliarella touched in the rebound from a Pepe shot that hit the post but Pozzi then headed in his second goal in the 73rd to deny the hosts victory.
"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.
Lazio claimed their first points by beating visitors Bologna 3-1, Fiorentina went down 1-0 at Lecce and Catania prevailed 2-1 against Parma in Sicily.
Promoted Brescia beat visiting Palermo 3-2 in a match that started at the new 10:30am GMT kick-off slot.
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