Second-placed Milan were on top for most of the match and Klaas-Jan Huntelaar headed over a glorious chance to break the deadlock in the closing stages.
Juventus boosted their Champions League qualification hopes with a 2-1 victory at Fiorentina that lifted them to fourth.
Marco Borriello blasted wide a good chance set up by Ronaldinho's threaded pass and Roma defender Nicolas Burdisso was lucky an attempt to head away a Mathieu Flamini cross did not fly into his own net.
The visitors continued to make the running after the break and Roma's Julio Sergio just managed to scramble the ball away in the 55th when Borriello burst into the area and aimed inside the near post.
Milan coach Leonardo had sprung a surprise by giving Huntelaar injured Alexandre Pato's place in his attacking trident rather than David Beckham, who set up a good chance for Ronaldinho after coming on in the 72nd minute.
The England midfielder will hope he was being rested for Wednesday's visit to his former club Manchester United in the Champions League last 16, when Milan need to reverse a 3-2 deficit.
Juve's Brazilian playmaker Diego had dribbled past keeper Sebastien Frey and slotted into an empty net to give the visitors the lead in the second minute after Antonio Candreva had sprung the offside trap with a smart pass.
