Serie A champions Juventus have picked up their seventh consecutive league victory to move within one point of becoming the first team to break the 100-point barrier in Italian football history.
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It was the hosts who threatened first, however, coming close midway through the opening half when Francesco Totti's volley from the edge of the box flew narrowly over the bar.
Llorente came close again with 10 minutes remaining of the half, but this time he couldn't keep his shot down having latched on to a pass inside the area.
Roma had a chance of their own to break the deadlock five minutes later as Gervinho weaved his way past a number of tackles and into a shooting position, but his subsequent effort was straight at Marco Storari.
The visitors almost grabbed the opener right on the stroke of half time when Paul Pogba poked the ball towards goal from inside the box, but his effort came back off the post.
Roma had the first chance of the second half when Vassilis Torosidis was played through on goal, but with only the keeper to beat he was denied by Storari.
Skorupski in the Roma goal was also called into action with 20 minutes of the match remaining, pulling off a fine stop to deny Llorente once again.
Pogba then threatened late on before the opener finally came in the 94th minute as Stephan Lichtsteiner's pass found Osvaldo, who fired a first-time effort home to give his side the win that sees them overtake Inter Milan's previous single-season points record of 97.