Inter qualify for Italian Cup quarters
The Serie A leaders, who will meet Juventus or Napoli in the next round, had two decent chances in the first half but the visitors deserved to be level at the break.
Dutch playmaker Sneijder, who has not lost in an Inter shirt since signing from Real Madrid in August but was sent off in the 1-1 Serie A draw at Atalanta on Sunday, then fired in on 60 minutes to break the deadlock.
Coach Jose Mourinho rotated his squad slightly but still included some of his big hitters as he battles to fight off a storm over his verbal abuse of a journalist on Sunday.
Inter were playing in their first game of this season's Cup, a much-maligned competition which fails to excite the Italian public.
The rest of the last 16 fixtures take place in mid-January when holders Lazio host Palermo.