The Biancocelesti were the happier side in the derby and have moved closer to the top of the table as Udinese dropped two points in the visit of Atalanta
Edy Reja's men took an early lead, thanks to a Hernanes penalty after home goalkeeper Maarten Stekelenburg was dismissed for fouling Miroslav Klose.
Roma equalised almost immediately after through Fabio Borini, but Stefano Mauri gave Lazio the points in the second half, and clinch their second league win over their rivals this season.
Luis Enrique's men got off to a nightmare start, being reduced to 10 men just six minutes into the game as Stekelenburg saw red for bringing down Klose inside the box when the striker was trying to round the Dutch custodian.
Bogdan Lobont was introduced to defend Roma's goal, replacing Erik Lamela, but the Romanian was sent the wrong way by Hernanes, who made no mistake from the spot.
It was certainly not the start that Luis Enrique had planned for his side, but Lazio's goal prompted a rousing response from his players.
After a Francesco Totti free-kick was blocked, the ball was sent to the far post to Juan. The Brazilian stopper’s left-footed shot smashed off the crossbar, but Borini was on hand to head the ball home. Biava tried to clear, but he did so beyond the line, and the goal stood.
The pace of the match dropped considerably after the leveller, as the Giallorossi looked content to frustrate due to their man disadvantage. Lazio were unable to capitalise on that fact, and they went into half-time with four of their players booked.
Totti gave the first warning in the second half, with a powerful long shot in the 58th minute that went wide of the goal, but Lazio responded in convincing fashion by retaking the lead through Mauri.
Cristian Ledesma sent a free-kick into the box for the Italian to guide the ball past Lobont with a sublime finish as Juan failed to get his head to the cross.
Lazio were now in the driving seat, and they almost doubled their lead just minutes later, when Fabio Simplicio gave the ball away to Hernanes with a misplaced pass. The Brazilian midfielder ran towards the box and as he was about to shoot, Juan stole the ball from under his nose with a perfect sliding tackle inside the box.In the 86th minute, Lazio had a player sent off to even the numbers, as Lionel Scaloni saw his second yellow of the match, but the Biancocelesti were able to keep hold of the lead and move up to third in the Serie A table as Udinese were frustrated by Atalanta.