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It was Destro who would give Roma the lead in the 10th minute as he was picked out by Alessandro Florenzi at the back post, before slotting an effort into the net.
They scored a second goal just three minutes later when Gervinho poked a ball through to Florenzi and the midfielder fired in a strike at the near post.
Cagliari threatened Roma's goal for the first time midway through the half as Luca Ceppitelli connected with a free kick at the back post, but he could only place his header wide.
The visitors fashioned one more scoring opportunity before the break, with Victor Ibarbo only able to direct a header wide of the far post.
In the second half, Roma continued to dominate and Maicon narrowly missed the top corner with a powerful strike from range.
Morgan De Sanctis was forced into his first save with 11 minutes of the match left as he tipped Samuele Longo's powerful attempt over the bar, and that proved to be the last chance as Roma held on to move to the top of the table.