Del Piero, used sparingly by Juventus coach Antonio Conte recently, came off the bench to slot home the second goal from Arturo Vidal's incisive pass after Martin Caceres had given them the lead just before the hour.
It was his second goal in five days after he scored in their Italian Cup semi-final against AC Milan in which a 2-2 draw sent Juventus to the final 4-3 on aggregate.
Inter, now almost certain to miss out on the Champions League, had the better of the first half but were foiled by world-class goalkeeping from Buffon.
Claudio Ranieri's team are ninth in the table with 41 points, 10 adrift of third-placed Lazio in the Champions League play-off spot.
Juventus, still unbeaten in all competitions this season, have 59 points from 29 games, four behind leaders AC Milan who beat AS Roma 2-1 on Saturday. There are nine rounds of matches to play.
"Del Piero deserves everything, he has shown himself to be an outstanding professional, he has accepted this [substitute] role without causing a controversy and now he is being repaid," Buffon told the Juventus website.
"It's a bitter defeat because it was a good, lively game against a Juventus side who deserve to be where they are," said Inter coach Claudio Ranieri.
"I'm very satisfied with the first hour of the game and extremely disappointed with the way we conceded the goal."
Lazio strengthened their grip on third place and a Champions League qualifying spot with a late win over Cagliari and Napoli squandered a two-goal lead in a 2-2 draw at home to Catania.
Mobido Diakite struck in the 88th minute, heading in from Cristian Ledesma's free-kick, to give Lazio a 1-0 win over the Sardinians, leaving them with 51 points and a three-point cushion over Napoli and Udinese.
Blerim Dzemaili and Edinson Cavani scored in a seven-minute spell to put Napoli in command against Catania, only for Nicolas Spolli and Davide Lanzafame to reply following corners in the final 20 minutes.
Napoli, who reached the Champions League last 16 this season, were left on 48 points, level with Udinese who drew 1-1 at Palermo.
There was little change at the bottom with a flurry of draws keeping Lecce, Novara and Cesena as firm favourites for the drop.
Lecce, 18th in the 20-team table, have 27 points, five adrift of safety, after a goalless draw against Novara, who are three points and one place behind them.
Cesena are a further six adrift at the bottom after a 2-2 draw with 17th-placed Parma (32 points).
Siena, who drew 1-1 at Chievo, and Fiorentina, held 2-2 at Genoa after Rodrigo Palacio scored an 89th-minute equaliser for the hosts, are both on 33 points
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