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The hosts almost took the lead in the 16th minute when Mattia Destro let fly from range, drawing a smart stop from the keeper to deny the Italian striker.
Roma doubled their lead right on the half-hour mark when Gervinho did brilliantly to set up Destro, who coolly rounded the keeper before sliding his finish into an empty net.
The visitors again had a chance to pull a goal back shortly afterwards, but they squandered the opportunity once more as De Sanctis denied Antonio Di Natale's strike.
They did finally register on the scoreboard just six minutes after the restart when Giampiero Pinzi picked the ball up in midfield before driving forward to the edge of the box and drilling an effort into the bottom far corner.
They could have levelled things up in the 55th minute when Di Natale drilled a low effort towards the corner, but once again the veteran striker was denied by De Sanctis.
Totti then came close to bagging a second of the evening when he fizzed a strike narrowly wide, but he turned provider for Roma's third later in the half, giving the ball to Vassilios Torosidis, who did the rest with a fine finish from outside the area.
Di Natale had another chance to reduce the deficit back to one goal two minutes later, but his powerful strike from the edge of the box was saved by De Sanctis, who once again came out on top in their personal duel.
The visitors could not complete their comeback, however, as Roma held out for a victory that keeps them three points clear of Napoli.