Jordan Veretout and Edin Dzeko scored the first half goals for the Giallorossi, as Matteo Pessina's finish just moments into the second half proved not quite enough for the dogged visitors.
Veretout converted from the penalty spot just 10 minutes into the match, taking full advantage after Lorenzo Pellegrini had been felled inside the box.
Then, in the dying seconds of the first half, it was Dzeko who doubled the advantage - the striker planting his header, from Leonardo Spinazzola's weighted cross, beyond the despairing goalkeeper.
In the process, the Bosnian became the club's all-time leading foreign goalscorer, surpassing the Argentine-born Pedro Manfredini with 105 for the club.
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At that stage Paulo Fonseca's side looked to be cruising, although all that changed just minutes into the second half - as Pessina finished brilliantly inside the box to halve the deficit.
That set up an attritional final 40 minutes of the contest, with the Giallorossi often forced into some sustained periods of defending in order to keep the visitors at bay.
That is not to say they didn't have chances of their own, however: Dzeko himself was guilty of wasting a couple, while Henrikh Mkhitaryan hit the post early in the match and saw another attempt somehow cleared off the line later on.
Nevertheless, the Giallorossi held on for victory - building on last week's triumphs against Parma and Brescia.
They are back in action, once again at the Olimpico, on Sunday as Inter Milan come to town.
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