Inter join Palermo in Italian Cup Final
Cameroon striker Samuel Eto'o expertly opened the scoring for Inter at the San Siro following good work by Houssine Kharja and McDonald Mariga on 58 minutes.
Marco Borriello hit the post for the visitors before heading in Simone Perrotta's cross six minutes from time to spark a nervy finish for Inter who held on as even Roma keeper Doni stormed up field.
But it was always a tough ask for Roma following Dejan Stankovic's winner in the first leg and Inter's eagerness to progress in the Cup having lost their Serie A and Champions League titles.
Milan, who sealed the scudetto at the weekend to end Inter's five-year reign as champions, failed in their bid for a first domestic double when they lost 2-1 at Palermo on Tuesday.
Inter captain Javier Zanetti was making his 1,000th professional career appearance and will hope to celebrate the club's seventh Italian Cup against the Sicilians in Rome on May 29.