Following Juve's goalless draw at Fiorentina on Friday, Roma had the chance to cut the gap at the top to just a point, however, striker Simone Zaza's double put visitors Sassuolo in command at the Stadio Olimpico.
Zaza opened the scoring in the 15th minute when he charged down a clearance from Roma goalkeeper Morgan De Sanctis, who had signed a new contract earlier in the week, the 23-year-old profiting from his endeavour as the ball cannoned into the net.
The Italy international found the target in more conventional fashion three minutes later, latching on to Simone Missiroli's ball over the top and slamming beyond De Sanctis.
Matters worsened for Roma five minutes into the second half as Daniele De Rossi was sent off for a second bookable offence but they were given a lifeline 12 minutes from time when Ljajic rolled the ball home from the penalty spot after Sime Vrsaljko had handled in the area.
Roma pressed to try and find a leveller and were rewarded in the third minute of injury time, Serbian forward Ljajic converting from Alessandro Florenzi's low right-wing cross to ensure a share of the spoils before Vrsaljko received his second caution and was dismissed.
Meanwhile, Torino twice came from behind to ensure a 2-2 draw against Palermo.
Paulo Dybala restored Palermo's advantage in the 43rd minute after Venezuelan forward Josef Martinez had cancelled out Luca Rigoni's 16th-minute opener.
But again the Sicilians could not hold on to their lead and Torino captain Kamil Glik headed home in the 63rd minute to earn a point for the home side.
