Both sides made nine changes with one eye on the top of the table Premier League clash between the same two sides on Saturday.
But Maurizio Sarri's gamble on throwing on Hazard 10 minutes into the second half paid off as Emerson Palmieri levelled from his free-kick 11 minutes from time before the Belgian's wonderful solo effort won the tie.
"Not only is he one of the best in the Premier League — if not the best — but he is one of the best in Europe and the world," said Zola, himself a Chelsea legend as a player. In my opinion we haven't seen the best of him yet. He's remarkable."
Daniel Sturridge looked set to haunt his former employers by opening the scoring for Liverpool shortly after he had missed an open goal early in the second-half.
Giroud, Morata fight for Chelsea starting spot
But Liverpool manager Jurgen Klopp, who took charge three years ago next month, will now have to wait until at least May to deliver his first trophy since arriving at Anfield as another chance of silverware slipped by with his side's first defeat of the season.
"This is good preparation for Saturday but we have to defend better," said Klopp.
It was another frustrating night for Alvaro Morata, though, as the Chelsea striker failed to make the impact Sturridge did at the other end.
Morata's best chance came inside 20 minutes when the Spaniard latched onto Cesc Fabregas's pass over the top.
Simon Mignolet did well to divert Morata's initial chipped effort before he dragged the rebound across goal and beyond the far post.
Liverpool took longer to adjust to the wholesale changes with £47 million ($58 million) signing Fabinho making his full debut in midfield, while Dejan Lovren made his first appearance of the season in central defence after playing a full part as Croatia reached the World Cup final.
However, they dominated the early stages of the second period and should have been in front when Sturridge rounded Willy Caballero, but somehow skewed wide with the goal at his mercy.
Sarri introduced Hazard with 35 minutes remaining, but moments later his side were behind as Sturridge made amends in spectacular fashion with an overhead kick after Caballero parried Naby Keita's drive.
Hazard showed his class to strike the winner as he danced past five Liverpool challenges before crashing a rising shot into the far corner for his sixth goal of the season.
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