Roberto Donadoni's men began the day in seventh - needing to move up a spot to claim European qualification - and did what they needed to do by winning 2-0 thanks to a second-half brace from Amauri.
However, Parma would have been denied a Europa League place had Torino's Alessio Cerci not failed to convert an injury-time penalty as his side were held to a 2-2 draw by Fiorentina.
On a Sunday packed with twists and turns, Torino's hopes looked to have been dashed when Ante Rebic put Fiorentina 2-1 up with 11 minutes remaining.
However, Jasmin Kurtic levelled six minutes from time before Cerci - one of the stars of Torino's campaign - saw a penalty saved by Antonio Rosati.
Parma's triumph made Milan's result irrelevant but the San Siro club rounded off their campaign with a 2-1 home win over Sassuolo.
An Andrea Pirlo free-kick found the net via crossbar and Cagliari goalkeeper Marco Silvestri in the eighth minute, before further first-half goals from Fernando Llorente and Claudio Marchisio enabled Antonio Conte's men to cruise to victory.
Juve became the first team to win all their home matches in a Serie A season, while also breaking the 100-point barrier.
Roma, who failed to keep pace with Juve over the campaign, ended their season with a disappointing 1-0 loss to Genoa, while third-placed Napoli hammered Verona 5-1 with Duvan Zapata and Dries Mertens weighing in with a brace each.
Victor Obinna took the shine off Javier Zanetti's final Inter game, scoring twice against his former club in a 2-1 win for Chievo.
