The much-changed home side had to come from two goals down to secure a draw, with the Serbia international netting a penalty and an injury time goal
Two quick goals from Simone Zaza in the first half gave the visitors the lead, the Italy international first capitalising on a terrible mistake from goalkeeper Morgan de Sanctis to open the scoring, before an emphatic finish saw him double his side's lead just minutes later.
The win seemed imminent for Sassuolo until the late stages, when a penalty in the 78th minute allowed Ljajic to halve the defecit and then an injury-time strike from the 23-year-old saved his side's blushes and secured a point to ensure they stayed within three points of Juventus, who drew 0-0 with Fiorentina on Friday.
While Roma completely dominated possession throughout the game, they failed to stretch or get the better of the Sassuolo defence for most of the clash, as the opponents were organised incredibly well and stacked with players who threw themselves in front of the ball to block the opponents' shots on goal.
It was a close escape for coach Rudi Garcia, whose attention was clearly on Wednesday's crucial Champions League tie with Manchester City.
The Giallorossi boss made six changes to the starting XI which beat Inter 4-2 in the previous game, with Alessandro Florenzi, Mapou Yanga-Mbiwa, Daniele de Rossi, Mattia Destro and Juan Iturbe coming into the first-team, while Kevin Strootman made his first start for nine months.
After a quiet opening 15 minutes, the game was sparked into life when Zaza gave the visitors the lead.
Yanga-Mbiwa passed the ball back to De Sanctis, who took his time despite Zaza closing in. As the keeper went to clear it from deep in the box, the forward slid in and blocked it, sending it straight into the net.
It took only three minutes for that lead to be doubled, with the visitors’ high line being caught out by a Simone Missiroli through ball and Zaza was able to take it on and fire past De Sanctis easily.
The 23-year-old had a chance to complete his hat-trick in the 23rd minute, latching onto another pass and bursting into the box, only to be caught by the Roma defence who snuffed out the attack.
Jose Holebas, who scored in the previous week’s win over Inter, came close to halving the deficit, driving down the left side and unleashing a dangerous shot which struck the bar.
Mattia Destro saw a promising attack come to an end due to his own poor first touch and the striker scuppered another opportunity when a nice cross from Florenzi found him in space in the box, but the header went wide.
While a dangerous attacking outlet for Roma, Holebas put in some incredible defending to prevent a third goal for the away side, sliding in to knock the ball out as the opposing attackers were queueing up to hit it.
The second half started terribly for the hosts, with Daniele de Rossi being dismissed after five minutes with a second yellow card. The midfielder had been booked in the first period for pulling Sansone to the ground and his second came after bringing down Domenico Berardi in the middle of the park.
The visitors began to put more pressure on Garcia’s men and opened up a great chance in the 57th minute, with Zaza flicking it on to Berardi whose shot from the edge of the box was saved.
Garcia sent Radja Nainggolan and Gervinho on for Strootman and Iturbe as he looked to ensure his side created more chances, but the space between the defence and midfield was incredibly tight and the backline proved impossible to stretch.
Gervinho’s dribbling ability and close control saw him weave his way into some promising spaces and he eventually had a massive influence when he drove into the box to see a shot hit the hand of Sime Vrsaljko, with the referee pointing to the spot. It seemed a harsh decision from the referee as the defender was sliding in and had no time to avoid the ball, but Ljajic stepped up to send it straight down the middle and into the net.
The intensity from Roma increased even further as they looked to get at least a point from the clash, but Sassuolo continued to match them everywhere, making sure Gervinho was kept at a manageable whenever the lively Ivorian got on the ball.
A ball over the top into the box from substitute Seydou Keita was tracked well by central defender Paolo Cannavaro, who leapt up and lifted his leg high to clear it in a desperate move.
Shortly after, Ljajic dribbled into the box and squared it to Florenzi who looked set to pull the trigger and blast home the equaliser but Francesco Acerbi stuck a leg out to block it and Nainggolan sent it over the bar.
It was a last gasp stretch from Acerbi right at the death which epitomised the fight and determination from Sassuolo, but their heroics were not rewarded with all three points as Ljajic popped up with goal right at the death, bursting in to the back post to send a loose ball into the net.