Edin Dzeko had looked set to enjoy one of the most memorable nights of his career after he scored twice – including one of the all-time great Champions League goals – to help Roma rally from 2-0 down to lead 3-2 with 20 minutes remaining.
However, Hazard spoiled the party for the Italians with an equaliser five minutes later in the Group C clash in London on Wednesday.
Going into the game on the back of two Premier League consecutive defeats, Chelsea quickly allayed any nerves around Stamford Bridge when David Luiz guided a sweetly struck shot into the net after 11 minutes and Hazard doubled their lead, turning an Alvaro Morata pass into the net eight minutes before half-time.
But Roma were never out of the contest and Aleksandar Kolarov's goal five minutes prior to the break gave them hope of a second-half reprisal that came true when Dzeko scored a stunning volley and a header to give them the lead.
The contest swung from end to end throughout and even at 3-3 there were numerous chances for both sides to find a winner, but a stalemate seemed fitting after Hazard and Dzeko matched each other goal for goal and inspired their sides in equal measure.
Returning from injury, Morata fired straight into the arms of goalkeeper Alisson when Hazard played him through on goal in the fifth minute, but the visitors refused to sit back and Diego Perotti went on a mazy dribble through Chelsea's defence three minutes later.
Errors began to creep into Roma's defensive play and after his ball into the box for Morata was blocked by Juan Jesus, David Luiz ran onto the rebound and stroked it beyond Alisson into the bottom right corner of the net from 20 yards.
Just as Roma began to make gains in midfield, Chelsea broke at the other end and Morata's deflected pass looped over to the far post where Hazard was on hand to tuck the ball into the net from close range.
But three minutes later Kolarov, who picked up the ball on the left wing, rounded Cesar Azpilicueta and rattled in a shot that hit the top of the net via a slight touch by Andreas Christensen.
In the second half, Dzeko came within a whisker of turning a Kolarov cross into the net as it flashed past his toes inside the six-yard box.
Perotti then curled a shot into Thibaut Courtois' hands with half an hour left to play, before a moment of brilliance changed the complexion of the game.
Federico Fazio jogged over the half-way line and played a long, chipped pass forward and Dzeko watched it all the way into the box before meeting it with his boot laces and volleying an unstoppable shot over the head of Courtois.
Chelsea had barely reacted to the blow when Dzeko scored again six minutes later, applying a glancing header to Kolarov's free-kick to take it past Courtois and into the far corner of the net from six yards out.
If Roma head coach Eusebio Di Francesco was delighted with that, he will have been equally appalled by the simple nature of Hazard's equaliser.
The Belgian forward was left unmarked when second-half substitute Pedro sent over a routine cross, and Hazard's header found the bottom left corner of the net with accuracy, prompting a scramble for chances in the last 15 minutes but neither side could force a winner.
Key Opta facts:
- Roma have never won an away game against English opposition in the Champions League (D3 L6).
- Eden Hazard scored his first Champions League goals since March 11th 2015 versus PSG – 952 days ago.
- Hazard's two goals were more than he had managed in his previous 14 games in all competitions for Chelsea (1).
- This is the first time that a team managed by Antonio Conte has conceded three goals in a Champions League game.
- Chelsea have scored four goals from outside the box in the Champions League this season, more than any other team.
- Roma have failed to keep a clean sheet in their last 23 away games in the Champions League.