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Alvaro Pereira was the first to test the keeper for the visitors, but his effort was comfortably kept out by Nicola Petrovic.
Rodrigo Palacio came on for Inter at half-time and, within six minutes, had given them the lead when he latched on to Fredy Guarin's pass.
Inter doubled this lead with 15 minutes left, Palacio and Guarin teaming up again before the former netted his second of the game.
Guarin got his own name on the scoresheet late on having been found by Antonio Cassano to put the game well and truly beyond doubt.
Partizan grabbed a late consolation goal through Nemanja Tomic, but it was too little too late as Inter ran out 3-1 winners.