Sergej Milinkovic-Savic and Ciro Immobile scored in each half for Lazio, who last beat their neighbours in the Italian Cup final in May 2013, at a disappointingly half-empty Stadio Olimpico.
Roma defender Anthony Rudiger was repeatedly subjected to racist chanting from Lazio fans during the first half, prompting the stadium announcer to warn that the match would be interrupted if it continued. The chanting died down after that.
The Roma end of the stadium remained deserted as the supporters continued their boycott in protest at partitions which have been installed on the Curva Sud (South Curve).
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Authorities had lowered the partitions as a compromise measure but Roma fans want them removed altogether, saying the barriers limit their view of the pitch and divide groups of supporters who used to sit together.
They also say they have been banned from waving flags and banners and get fined for sitting in the wrong seats.
Roma midfielder Radja Nainggolan, the team's driving force this season, had a relatively subdued match while Lazio looked lively.
Officially the home side at the stadium shared by the two teams, Lazio went ahead when Felipe Anderson burst down the right and pulled the ball back for Milinkovic-Savic to fire into the roof of the net on the half hour.
The second goal came from a similar move as Keita Balde Diao got away from his marker on the right and slipped the ball to Immobile to score from close range in the 77th minute.
Roma had won five of the last seven meetings, all in Serie A, while the other two matches were drawn.
(Writing by Brian Homewood in Berne; Editing by Toby Davis)
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