The Belgium international was introduced to the game with his Blues side trailing in the second half before he burst through the Reds defence to thunder an effort past a helpless Simon Mignolet to steal the tie.
The hosts took the lead early in the second when Daniel Sturridge's acrobatic scissor kick fired Jürgen Klopp's side ahead against the Reds strikers former team.
Chelsea leveled the contest through Emerson Palmieri's close-range finish after Ross Barkley's thunderous header was parried away by Mignotlet as the Italy international tapped home to level.
The goal needed intervention from the video assistant referee (VAR) to check for offside before being awarded.
The Premier League leaders will be looking for revenge when the two sides meet again domestically on Saturday (kick-off 17:30 BST), while the fourth-round draw takes place on the same day at 21:00 BST.
Cagey first-half ends goalless
Despite numerous changes to both English heavyweights, it was the visitors who asserted an early dominance.
Cesc Fabregas controlled the middle of the park finding pockets of space for both Willian and Victor Moses to threaten down both flanks.
An early wave of Chelsea pressure was eventually subdued when Naby Keita fired a fierce effort into the arms of Willy Caballero.
Willian got an early roar from the Anfield crowd when his free-kick rocketed into the Kop grandstand.
Alvaro Morato saw a huge chance go begging when the Spanish forward was let loose by his compatriot Fabregas with a fabulously lofted pass before the former Real Madrid striker was denied by Mignolet and then the rebound was left unpunished by Willian.
Another effort from Morata forced Mignolet into another save - this time the pass coming from Willian - who found his teammate running past the Liverpool back-four before having another effort denied by the Belgian international.
Referee Kevin Friend resisted the temptation to allow his VAR assistants to intervene when Keita went down following a clash with Gary Cahill.
It proved to be an expert call as the proposed foul saw no contact and left Liverpool's midfielder lucky to walk away without a card for simulation.
Joel Matip was drawn into a booking when his sloppy foul stopped an imminent Blues counter-attack before another free-kick was swept up by Mignolet.
Keita once again was denied by Chelsea's Argentine keeper on the night as his curled right-footed shot was well saved before going out for a corner.
The Reds came to life before the end of the first half when a well-worked move saw Xherdan Shaqiri found Sadio Mane with a looming cross before the Senegalese ace headed into the arms of Caballero.
Shaqiri's second competitive start saw the former Potter exuding confidence when his 30-yard-effort went towering over the Chelsea bar.
Sturridge avenges horrendous miss to fire hosts in front
A ludicrous start to the second half saw Liverpool supporters completely bewildered to how they weren't ahead in the opening seconds.
Andreas Christensen played a blind backpass, sending Sturridge clean through on goal with the former Blue looking to capitalise on the Chelsea defenders error.
The Liverpool forward skipped around Caballero, who got a tiny touch on the ball; however, Sturridge still had an open goal at the Kop End but astonishingly sent it wide.
Chelsea reacted quickly to their early error as the visitors almost found an early lead moments after Sturridge's shocking miss.
Willian drilled a peach of a ball with the outside of his right foot and Morata was unmarked to nod his effort over from about eight yards out.
The Chelsea curse which befell Andriy Shevchenko and Fernando Torres seemed to have struck again when the 25-year-old forward sent another effort begging.
Another gift went begging for Klopp's side when Barkley carelessly headed back towards his keeper before Mane was lurking goalwards. However, the Chelsea shot-stopper came to the visitor's rescue again to keep the hosts at bay.
The Reds, soon found their desired pressing game in the second period and their endeavours were rewarded when Premier League veteran James Milner forced Fabregas into a mistake gifting the ball to Mane who found Keita who looked goalbound.
The former Bundesliga star drove another effort at Caballero who once again parried his shot away before Sturridge was left unmarked again with the goal in his grasp.
The 29-year-old striker didn't require a second invitation as his superbly executed scissor-kick left his former team ruing their error as the rejuvenated Sturridge fired the hosts in front.
Another penalty appeal was waved away for the Reds when Shaqiri cut inside and went to ground. A soft touch on the Swiss star's shoulder didn't quite merit anything worthy of a spot-kick.
Blues level before Hazard steals the show
Chelsea responded to the setback to dent Liverpool's 100 per cent record when a Fabregas free-kick flew over the Reds high line before Barkley cannoned his header at Mignolet before Emerson tapped home to level for the visitors.
Sturridge almost doubled his tally on the night towards the end of the match when his left-footed effort rattled the Chelsea crossbar as a Reds winning goal came agonisingly close.
It proved to be a significant moment in the game as the moment of the match quickly followed Sturridge's miss when substitute Hazard produced a moment of utter class when his solo effort snatched the victory for Sarri's Blues.
The Belgium superstar dazzled through Keita before bewildering Alberto Moreno to cut onto his right and rifle his effort past Mignolet to send the Chelsea supporters into delirium.
A goal worthy of winning any match and a fitting way to crush Liverpool's unbeaten start to the season as the two sides will turn their attention to Saturday's rematch as both giants look to protect their Premier League unbeaten status'