Having grown frustrated by his squad's inability to score, Roma coach Rudi Garcia was sent off for protests in the 72nd and watched the end of the match from the stands.
Cagliari moved level with struggling AC Milan in 13th place.
The match was moved to Monday to let the pitch recover from Saturday's Italy-Argentina rugby test.
Roma dominated the first half but couldn't quite find the target.
Gervinho, Maicon, Kevin Strootman and Dodo each had chances in the opening 10 minutes.
In the 39th, Strootman collected a pass behind the defense and had only the goalkeeper to beat but Cagliari 'keeper Vlada Avramov saved his shot by the near post.
Cagliari threatened with a header from Victor Ibarbo in the 34th but Roma goalkeeper Morgan De Sanctis made a diving save.
Roma again took the initiative after halftime but Avramov made a spectacular save on a long shot from Maicon in the 51st.
A header from Cagliari forward Marco Sau found the net but was waved off for offside in the 54th.
Roma defender Mehdi Benatia limped off with an apparent injury in the final minutes and Avramov preserved the draw by stopping a close-range header from De Rossi in added time.
Avramov "was the best player on the pitch," De Rossi said.
A minute of silence was observed before the match in memory of the victims of recent flooding in Sardinia, and Roma wore black armbands in memory of Amedeo Amadei, the center forward of the Giallorossi squad that won the 1942 Serie A title. Amadei died Sunday at age 92.
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