Daniele De Rossi, given a rare start by Roma, was sent off seconds before half-time for punching Stefano Mauri in the face as they tussled for the ball in the penalty area and Mauri was also dismissed late in the game for a second yellow card.
Alexandre Pato missed a first-half penalty as Milan's brief revival ended with a 3-1 home defeat by fourth-placed Fiorentina, and third-placed Napoli scored three times in the last 15 minutes in a 4-2 win at Genoa.
Second-placed Inter Milan's run of 10 consecutive wins ended in a 3-2 defeat at Atalanta as they dropped four points behind leaders Juventus, who won 6-1 at Pescara on Saturday.
German Denis scored two second-half goals, including a penalty, for Atalanta to atone for scooping the ball over the goal from six yards in the first half.
Giacomo Bonaventura had given Atalanta a first-half lead and Fredy Guarin levelled from a free-kick before Denis sprang into action with a seven-minute brace. Rodrigo Palacio pulled one back with six minutes left.
Eighteen-year-old Argentine forward Paulo Dybala scored twice to give Palermo a 2-0 win over Sampdoria and hand the visitors their seventh consecutive league defeat.
Chievo and Udinese drew 2-2 after both scored in the last two minutes and Torino beat Bologna 1-0.
Juventus lead with 31 points from 12 games, followed by Inter (27), Napoli (26), Fiorentina (24) and Lazio (22).
Roma, who have the second best attack and joint worst defence in the lead, got off to a flying start when Erik Lamela met Francesco Totti's corner with a diving header to score his eighth goal of the season.
Torrential rain left puddles of water on the pitch, making it almost unplayable, and the conditions had a hand in Lazio's first two goals.
Antonio Candreva levelled in the 35th minute with a long-range free-kick which flew straight at goalkeeper Mauro Goicoechea but slipped through his hands and into the net.
Ten minutes later, Hernanes sent a low cross into the area, the ball was slowed down by a puddle and fell perfectly for Miroslav Klose to score from close range for the Germany striker's seventh goal of the season.
DRAMATIC FINALE
De Rossi, who has been left out of the line-up several times this season by coach Zdenek Zeman, started but was dismissed in first-half stoppage time for lashing out at Mauri.
It got worse for Roma immediately after the break when defender Ivan Pires headed an attempted clearance straight to Mauri and he lashed in the third.
In a dramatic finale, Mauri was sent off in the 85th minute before Miralem Pjanic's floated free-kick was totally misjudged by Federico Marchetti and flew into the goal.
Roma should have equalised in injury time but Pablo Osvaldo hooked wide from six metres after Michael Bradley chipped his cross over the Lazio defence.
Milan slumped to th
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
