After three successive draws in Serie A, Antonio Conte’s Inter were far from their best but still had enough to set up a last-four clash against Napoli.
The othert semi-final sees Juventus tackle AC Milan.
In a poor first half, Inter edged ahead just before the break when Antonio Candreva scored from close range after a pass from Lautaro Martinez who had made the most of a mix-up between Fiorentina’s Federico Ceccherini and goalkeeper Pietro Terracciano.
Martin Caceres headed the visitors level on the hour before Nicolo Barella settled the tie with a blistering volley seven minutes later.
Danish star Eriksen, signed on Tuesday from Tottenham for 22 million euros, was brought on as a substitute for Alexis Sanchez just before Barella’s strike.
“We did not intend to use Eriksen so soon, as he only started training with us yesterday, but Matias Vecino and Barella were the only available midfielders,” said Conte.
“Eriksen has character and raises the quality level.”
Fellow new recruit Victor Moses, signed on loan from Chelsea, also made a second half appearance for Inter.
AC Milan booked their place in the two-legged semi-finals after beating Torino 4-2 on Tuesday to continue their Zlatan Ibrahimovic-inspired revival.
Extra-time goals from substitutes Hakan Calhanoglu and Zlatan Ibrahimovic sealed passage into the last-four.
They will be relishing the tie with Italian champions Juventus, who thumped Roma 3-0 in their quarter-final.
Napoli defeated Lazio 1-0 in their quarter-final last week.
