Rudi Garcia had seen his side's title tilt falter in recent weeks, going on a run of four draws on the bounce, but a return to winning ways pulls Roma within seven points of leaders Juventus, who beat Milan 3-1 on Saturday.
Adem Ljajic powered into the roof of the net after some neat build-up play in the 37th minute, before Leandro Paredes doubled the advantage with a driven half-volley five minutes from time.
Paul-Jose M'Poku headed a late consolation for Cagliari but there was not enough time for the hosts to find an equaliser.
Napoli, who have now won four in a row, remain in touch with the top two following their 3-1 win at home to Udinese.
Fiorentina came out on top in a five-goal thriller at home to Atalanta, winning 3-2, and climb above Sampdoria after Sinisa Mihajlovic's men were held to a 1-1 draw by Sassuolo.
Elsewhere, Inter defeated Palermo 3-0 to register their first victory in four Serie A matches.
Roberto Mancini's men had suffered back-to-back defeats in their last two games – part of a run that saw Inter slip to 13th.
In the day's remaining fixture, Empoli boosted their survival hopes with a 2-0 win over lowly Cesena.
