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.
Juventus can reclaim the lead and go two clear at the top with a win at Genoa on Thursday.
MILAN BEATEN
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.
Mauricio Isla broke into the Milan box and when his effort came back off the post, Di Natale could not fail to score.
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.
Rookie coach Leonardo has already presided over two defeats from five league games this term but limited recruits in the transfer window mean the Brazilian has little room to manoeuvre.
Francesco Totti converted a late penalty to give AS Roma a thrilling 3-3 draw at Palermo in pouring Sicilian rain.
The pitch was so waterlogged that the ball often became stuck in puddles but Totti made sure he blasted the spotkick home.
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.
Conte was also sent to the stands for protesting late on.
