There are two Champions League places left to take in Italy behind league winners Juventus and second-placed Napoli.
Claudio Ranieri's side, semi-finalists in the elite European competition last season, are now fifth, three points behind Inter Milan, and one adrift of Atalanta who occupy fourth.
Both teams have difficult games to come this weekend with Inter Milan travelling to Napoli and Atalanta at champions Juventus, in a game which will be final match at home for coach Massimiliano Allegri.
AC Milan are just behind Ranieri's side and can overtake the Romans with a win at home against relegated Frosinone.
Torino are seventh, three points behind Roma, and can pull level with with a win at relegated Empoli.
Roma had their chances at Sassuolo with both Edin Dzeko and Justin Kluivert hitting the post.
Elsewhere, Domenico Criscito's late penalty grabbed a point for Genoa in a 1-1 draw against Cagliari to move two points above the relegation zone with one game to play.
Udinese's on-loan Watford striker Stefano Okaka scored a quick-fire brace in a 3-2 win over SPAL.