The away side levelled when Hazard, introduced two minutes before Sturridge's goal, delivered a free-kick into the Liverpool box, Barkley's header was palmed away by Mignolet and Emerson prodded in.
The first of two meetings between the clubs this week, with a Premier League clash at Stamford Bridge to come on Saturday, saw Liverpool boss Jurgen Klopp and Blues counterpart Maurizio Sarri both make eight changes to their starting line-ups.
Sturridge nearly restored Liverpool's lead after hitting the bar but it was Chelsea who snatched the victory as substitute Eden Hazard came off the bench to score a superb solo goal to make it 2-1 in the 85th minute.
Stunner: Chelsea's Eden Hazard (centre) celebrates with teammates after scoring the winning goal at Anfield.
"There will be a lot of discussions about VAR, it's not ideal - offside, the free-kick for the first goal", Klopp told Sky Sports.
Chelsea will face Liverpool once again on Saturday in the Premier League but Zola does not think Wednesday's result will influence the outcome at the weekend. The linesman is in a really good position.
'We scored a similar goal a few days ago and it's hard to defend at the end but it's, of course, better to defend.
Daniel Sturridge has now scored 11 goals in his last 11 appearances in the League Cup, and much like Danny Welbeck, the England worldwide is very much on the periphery of first-team action at his club, having fallen out of favour, but both strikers have asked questions tonight. Alvaro Morata got in behind the defence for the first big chance but was foiled by Simon Mignolet as he looked for a cheeky chipped finish. We wanted to win it, we feel unlucky, we hit the bar.
'Yes, of course we could have defended better.