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Totti himself went close to scoring five minutes later, but his left-footed shot from outside the box was saved by Federico Marchetti in the Lazio goal.
Then Antonio Candreva found the target with a direct free kick in the 35th minute to equalise for the Aquile.
It became 2-1 to Lazio in the 43rd minute when Hernanes set up Miroslav Klose for the German striker to fire in from the centre of the box.
To add insult to injury Mauri scored Lazio's third goal at the Stadio Olimpico two minutes into the second half.
Mauri set up Candreva in the 63rd minute, but his shot from the centre of the Roma box was saved by goalkeeper Mauro Goicoechea.
Roma also had a chance to add to the scoreline when Totti whipped in a delivery in the 66nd minute, but Pablo Osvaldo's header sailed over the Lazio crossbar.
The explosive Rome derby saw another dismissal late in the match, this time Mauri being sent off in the 85th minute for a second bookable offence.
A minute later Miralem Pjanic scored from a direct free kick to revive Roma's hopes of a point, but it proved to be a mere consolation.