Samuel Eto'o tapped in the first after Walter Samuel headed on a corner and strike partner Diego Milito soon beat the offside trap to score his fifth in five league games this term.
"To start like this, I could never have imagined it," the close-season signing from Genoa told Sky television.
"We had a fantastic first half. We've won and played well."
Lucio nodded in another corner after the half hour mark with Ezequiel Lavezzi pulling one back for Roberto Donadoni's side, who have picked up just four points so far despite spending big.
Inter went above this Saturday's opponents Sampdoria, who dropped points for the first time this term when headers from Stevan Jovetic and Alberto Gilardino either side of the break sealed Fiorentina's 2-0 home win.
AC Milan's inconsistent start to the campaign continued with a 1-0 loss at Udinese, where Antonio Di Natale scored midway through the first half.
The Italy striker also struck the post while Milan, who started with Ronaldinho on the bench and had Mathieu Flamini dismissed for a second booking late on, hit the bar through Alessandro Nesta's header.
Bottom side Atalanta drew 0-0 at home to Catania in Antonio Conte's first match in charge, which was slightly marred by scuffles between rival supporters in Bergamo before kickoff.
