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The legendary Italian scored just before the hour mark with a sensational strike that flew past Juve keeper Gianluigi Buffon.
Roma started the brighter of the two sides and perhaps should have been a goal up after 11 minutes when Miralem Pjanic sent Osvaldo through, but the striker could only hit the sidenetting after he rounded Buffon.
Two minutes later, the Serie A champions were claiming a penalty when the ball hit Daniele De Rossi on the hand from a corner, but their shouts were waved away.
Three minutes into the second half, Osvaldo was sent through once again, this time from Totti, with his finish bobbling the wrong side of Buffon's post.
The forward was again thwarted by Buffon on 57 minutes when he met Pjanic's in-swinging corner, only for the World Cup winner to save brilliantly.
However, there was little the Italian international could do about Totti's strike a minute later, when he flashed a shot high into the corner of the net after Pjanic's free kick was blocked by the Juve wall.
The home side should have doubled their lead on 65 minutes when a quick break saw Totti set up De Rossi, but the midfielder failed to make a good enough connection.