Goals from Thiago Motta, Diego Milito and Maicon gave Inter a 3-0 lead at half-time before Dejan Stankovic added a fourth midway through the second half.
To round off a miserable night for the Rossoneri, they also lost Gennaro Gattuso to a red card just before the interval.
In Saturday’s other match, Bari’s first game of the season in front of their own fans ended in disappointment as they were held to a goalless draw by Bologna.
Juve’s top summer signing opened his Serie A account in the 25th minute before Roma’s Daniele de Rossi equalised 10 minutes later.
Diego put Juve back in front in the 68th minute and Felipe Melo added a third in injury time as the Turin giants claimed their second win of the new campaign.
The triumph means that Ciro Ferrara has had a dream start in his first full campaign as Juve coach, the club he once played for.
Giampiero Ventura’s side came closest to breaking the deadlock through Vitali Kutuzov in the second half, but the teams had to settle for a point each to add to the draws they picked up on the opening day of the season last weekend.