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De Paul fired home early in the second half for the hosts, in what proved to be the decisive moment of the game.
The Giallorossi dominated the ball for long spells and had their chances, but in Udinese goalkeeper Juan Musso they found a shot-stopper in top form.
Stephan El Shaarawy and Aleksandar Kolarov both went close in the first half, while Udinese were left camped in their own half for much of the second period.
Eusebio Di Francesco's side do not have long to dwell on the result - they face Real Madrid in the Champions League on Tuesday night.
Click here for match statistics from the game.
UDINESE 1-0 ROMA
Goals: De Paul (54')
Udinese: Musso; Ekong, Nuytinck, Samir; Larsen, Fofana, Behrami, Mandragora, Ter Avest; De Paul, Pussetto.
Roma: Mirante; Santon, Fazio, J. Jesus, Kolarov; Cristante, Nzonzi; Kluivert, Lo. Pellegrini, El Shaarawy, Schick.
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