The second-placed visitors took a half-time lead through Mattia Destro before Michel Bastos added a second deep into second-half stoppage time to ensure a fourth straight win for Rudi Garcia's men.
The result saw Roma close the gap on Juve to 11 points ahead of the leaders' game at Napoli on Sunday evening, while second-bottom Sassuolo - who have won just once in the last 12 matches - remained five points adrift of safety.
The capital club started well and Destro had two chances in quick succession to hand them the lead.
His first close-range effort was thwarted when Sassuolo defender Pedro Mendes made a vital tackle, and moments later the Italy striker sent a header just wide of the right-hand post from Alessandro Florenzi's cross.
The hosts came back into the game minutes later and could have gone ahead had Nicola Sansone's shot not been tipped over the bar by Morgan De Sanctis.
Roma took the lead after 17 minutes when Radja Naingollan took the ball down the right and found Destro just outside the 18-yard box. He ran through and beat home goalkeeper Gianluca Pegolo with a neat chip.
Destro almost doubled their lead as the game approached the half-hour mark, but, after latching onto Daniele De Rossi's cross into the box, the 23-year-old fired wide.
Referee Nicola Rizzoli caused controversy 10 minutes before the break when he handed the home side a penalty after speaking with his assistant, before changing his mind when he was surrounded by Roma players as play was stopped for four minutes.
Nicola Sansone had played the ball inside the box and was brought down by Roma defender Mehdi Benatia, with the referee deciding on no penalty only to give the spot-kick after consulting his assistant.
But, after a scramble between players - in which the referee was surrounded by the Roma players - Rizzoli changed his mind again.
The hosts started the second half well and Sansone tried his luck from outside the box but his effort sailed over the bar, before Florenzi forced Pegolo into action as he punched away the Roma midfielder's shot.
Paolo Cannavaro and and Domenico Berardi came close to equalising for the home side as the half wore on before Roma doubled their lead in the sixth minute of added time.
Substitute Francesco Totti picked out Rodrigo Taddei, who sent the ball through to Bastos inside the box and he slotted into the bottom-right corner of Pegolo's net.