An Edinson Cavani penalty put Napoli ahead after 63 minutes, with Marek Hamsik ensuring victory seven minutes from time at the Stadio Olimpico.
Del Piero, restored to the Juve starting XI for the final game in an illustrious career at the club, did not find a fairytale finish and his side's disappointment was completed when Fabio Quagliarella was dismissed late on.
Napoli, who last tasted success with the 1990 league title, started positively, Juan Camilo Zuniga forcing a save from Marco Storari in the first minute and Cavani shooting wide moments later from Zuniga's corner.
Juve were struggling to get a foothold in the match and allowed Ezequiel Lavezzi the chance to strike at goal in the 10th minute only for his shot to squirm wide.
Juve's first opportunity came in the 17th minute, Morgan De Sanctis with a diving save to deny Claudio Marchisio.
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Napoli were the real attacking force though, with Cavani just failing to get on the end of Lavezzi's teasing cross and Gokhan Inler shooting high and wide from 30 yards.
Del Piero's first real sight of the target came just before the break, his free-kick kept out by De Sanctis.
He tried his luck again five minutes into the second half but was well wide.
Napoli broke the deadlock after 63 minutes, Storari taking down Lavezzi in the area and Cavani converting from the spot.
Juve's best chance of an equaliser fell to Simone Pepe, but once again De Sanctis was up to the task.
Hamsik put the result beyond doubt in the 83rd minute, Goran Pandev providing the assist following a brisk counter.
All that was left was for Quagliarella to see red for an elbow on Salvatore Aronica, leaving Napoli celebrating and 37-year-old Del Piero bowing out on a low note.