Argentina striker Diego Milito scuffed in the equaliser from Wesley Sneijder's pass and the Dutchman then poked in the winner in the 89th minute after waves of Inter pressure.
Former AC Milan forward Andriy Shevchenko, whose career nosedived under Inter coach Jose Mourinho at Chelsea, opened the scoring for the hosts in the 21st minute with a deflected effort.
Mourinho threw on midfielder Thiago Motta and forward Mario Balotelli at halftime and the visitors almost equalised immediately when Walter Samuel nodded wide while Samuel Eto'o went even closer with another header.
The Italian champions did not stop there and after Milito's shot from a tight angle had been saved, Sneijder reacted quickest to score from close range.
The game had been in doubt after Ukrainian authorities on Friday banned all public events and imposed restrictions on people's movements for a three-week period following a first death from H1N1 flu.
