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Both sides made a slow start to the match with chances few and far between, although the Nerazzurri were doing more of the pressing and were hogging possession at the San Siro.
Walter Mazzarri's side's effort and hard work finally paid off on the half-hour mark under fortuitous circumstances.
Jonathan drilled in a low cross from the right that Livorno goalkeeper Francesco Bardi came out to collect, but he failed to get a proper grasp of the ball and allowed it to trickle over the line for an own goal.
That increased the urgency among the Livorno players, who pushed forward in search of an equaliser, with Andrea Luci shooting wide from a good position on the edge of the Nerazzurri box.
Inter could have gone 2-0 up four minutes from time had Rodrigo Palacio's looping header from inside the visitors' box been on target.