It was a good start for Antonio Conte's side with Álvaro Morata's half-chance before David Luiz opened the scoring in some style before Hazard added a second in the 37th minute, Aleksandar Kolarov got one back on his return to England but The Blues remained just ahead at the break.
Eusebio Di Francesco's side came flying out of the traps for the second period as Edin Džeko's two goals managed to put Roma in the lead for the first time, but Hazard's header managed to save a point for The Blues.
Straight out of the top drawer
Conte will have been desperate for his side to get back on track after Saturday's 2-1 defeat to bottom side Crystal Palace, and they looked to be back to normal after an excellent start to the contest.
The big boost was the return of striker Morata who has had a great start to life at Stamford Bridge, he was through on goal as he received the ball from Hazard but it was clear that he was still rusty as he curled it into the arms of Alisson Becker.
It wasn't long before Chelsea managed to get ahead of their Italian counterparts and it was something special of Luiz, the Brazilian bombed forward as he looked to pick out Morata with the pass. It was initially blocked but the defender continued his run to get a second bite of the cherry, it was stellar from Luiz as he curled it beyond the reach of Becker and into the bottom corner.
Doubling it up
After Hazard's opener the clash became a lot more levelled as both sides look to make a significant difference, and with eight minutes to play Chelsea managed to double their lead.
The ball came to Morata who looked to make some space for the shot but his effort was blocked by Federico Fazio, but the deflection fell perfectly for Hazard to stab it home at the back post.
Shaking some nerves straight away
It looked to be plain sailing from that point onward for Conte's side, but the visitors weren't going to make it easy as they managed to pull one back moments after going two behind.
Kolarov certainly looked to impress on his return to England having left Manchester City in the summer as he left César Azpilicueta for dead, the Serbian continued to bomb forward and let rip with the deflection from Andreas Christensen took it into the roof of the net.
Turning it all around
Chelsea went into the break with their nerves jangled slightly and came out still looking shaky from Kolarov's effort, and Roma certainly took advantage of that as Džeko turned the tie on it's head.
Hev could have brought it level in the 54th minute as he looked certain to score from a tap-in as Kolarov drilled the ball into the area, but Thibaut Courtois did brilliantly to get a toe on it to take his cross away from the striker.
The Belgian goalkeeper could do nothing to prevent the equaliser ten minutes later however, it was simple enough as Fazio played the diagonal ball into the area and Džeko always had eyes on the prize as he fired the superb volley straight down the throat of Courtois who had no chance.
The game was fully tilted on it's head in the 70th minute as Džeko added his second and Roma's third, it was poor on Chelsea's behalf as the former Manchester City man managed to pull away from any marker and glance Kolarov's free-kick into the far corner.
Coming to the rescue once again
Chelsea looked shook down to their core by the Bosnian's influence, but if one man could turn it around it would be Hazard and he came to their rescue once again.
The Belgian did brilliantly off-the-ball to make some space as Pedro played in a great ball and a rare header from Hazard found it's way in at the far post much to the delight of the majority inside the Bridge.