The Delfini, second-tier champions last season, were always going to be up against it at the Stadio Adriatico and so it proved as Wesley Sneijder got Inter up and running with 17 minutes gone.
Diego Milito then caught them cold with a second two minutes later before Phillipe Coutinho wrapped things up for Andrea Stramaccioni's men.
Sampdoria made a winning return to Serie A with a shock 1-0 victory at AC Milan.
Andrea Costa scored the only goal of the game in the 58th minute and, although the Rossoneri hit the woodwork twice, their fans made their feelings clear at the final whistle.
Lazio also opened their campaign with a 1-0 victory at Atalanta, courtesy of Anderson Hernanes' 18th-minute goal.
Napoli's bid to improve on last term's top-five finish got off to a flying start with a 3-0 victory in Palermo.
Marek Hamsik, Christian Maggio and Edinson Cavani all scored for the Partenopei.
Chievo kicked off the new season with a workmanlike 2-0 victory over Bologna.
Talismanic skipper Sergio Pellissier opened the scoring for the hosts in the second half and Rinaldo Cruzado doubled the lead 11 minutes from full-time.
Second-half goals from Alexander Merkel and Ciro Immobile were enough to earn Genoa a routine 2-0 win over Cagliari.
Cristobal Jorquera missed a 17th-minute penalty for the hosts, but Merkel got things going six minutes after the break and Immobile finished things off with five minutes left.
Zdenek Zemen's return to Serie A as coach of Roma was not a winning one as his men played out a 2-2 draw with Catania.
Giovanni Marchese and Alejandro Gomez twice put the visitors in front but the Giallorossi responded with goals from Pablo Osvaldo and Nico Lopez.
Siena, who are trying to overturn a six-point deduction for their part in a match-fixing scandal, could only manage a goalless draw against newly promoted Torino.
On Saturday, defending champions Juventus got the season off to a winning start by beating Parma 2-0, while Stevan Jovetic grabbed a brace in Fiorentina's 2-1 triumph over Udinese.
Sunday's Serie A Results
Saturday's Serie A Results