Vassilis Torosidis came close to giving the home side the lead early on as he tried to head in twice after having a shot blocked, but he could not force it past the keeper.
Federico Agliardi was under pressure again before the end of the half as Destro appeared to be in again, but a miscued shot was well held by the keeper.
Alessandro Florenzi came close to doubling Roma's advantage with just under 20 minutes still to play as he rounded a couple of defenders before unleashing a low shot, but Agliardi was ready again.
The home side did manage to end Cesena's hope of a late comeback inside the last 10 minutes when Mapou Yanga-Mbiwa picked out Daniele De Rossi, who struck the ball on the turn for Roma's second of the night, putting the win beyond doubt.
With the league leaders losing this evening, the result leaves Roma level on goal difference as well as points with Juventus.