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.
Sulley Muntari and Nigel de Jong were on target for Milan, who saw Philippe Mexes and Mattia de Sciglio sent off in the second half either side of Paolo Cannavaro seeing red for Sassuolo.
Juventus capped off their third successive title-winning campaign in style with a 3-0 victory over Cagliari.
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.
Relegated Catania continued their late-season flourish by beating Atalanta 2-1, but there was no respite for Bologna as they went down to a late Lucas Biglia penalty against Lazio.