Eto'o propels Inter past Genoa
The Cameroon striker opened the scoring on 15 minutes and doubled his tally just before the break.
Houssine Kharja hit back with a penalty for the visitors but Kenya midfielder McDonald Mariga settled the tie before Giuseppe Sculli's late headed consolation.
New Inter boss Leonardo, who won his first two league games in charge, handed a home debut to new defender Andrea Ranocchia against his former club.
Earlier, a Fabrizio Miccoli penalty 10 minutes from time gave Palermo a 1-0 win at home to Chievo and set up a quarter-final meeting with Parma who defeated Fiorentina 2-1 last month to progress.
Juventus host Catania on Thursday when Gianluigi Buffon is expected to make his long-awaited return from injury with the remaining last 16 fixtures, including AS Roma v Lazio and AC Milan v Bari, taking place next week.