Inter's Italy striker Antonio Cassano and Colombia midfielder Fredy Guarin were on target in the second half for the 2011 cup winners.
AC Milan, Juventus, Catania and AS Roma had already booked their places in the last eight.
The quarter-final line-up will be completed on Wednesday when Lazio host Siena, Udinese welcome Fiorentina and Napoli entertain Bologna.
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