Maurizio Sarri's side enjoyed a 2-1 win at Anfield in the League Cup third round on Wednesday.
Liverpool have started with six wins in the Premier League and a victory in the Champions League but they were knocked out of the League Cup thanks to a superb solo goal from Hazard in the 85th minute.
Daniel Sturridge had put Liverpool in front before Emerson levelled for Chelsea in the 79th, after Simon Mignolet parried out a Ross Barkley header from a free kick whipped in by Hazard.
The Belgian forward, a 56th-minute substitute, won the game with a devastating finish after a powerful run in from the flank, leaving two Liverpool defenders behind before firing into the far corner.
The two teams face each other at Stamford Bridge on Saturday in the Premier League.
Elsewhere, West Ham United hammered fourth tier (League Two) Macclesfield Town 8-0 and Danny Welbeck scored twice as Arsenal beat Championship Brentford 3-1.
Eden Hazard just ended Liverpool. This goal is absolutely filthy. ???????? pic.twitter.com/ao7Dg2yXDn
— World Cup (@FlFAWC2018) 26 September 2018