Liverpool took the lead in the third round contest via a Daniel Sturridge overhead kick on the hour mark before Emerson levelled things up with just over 10 minutes to go at Anfield.
The stage was set for someone to step up and be the hero and Hazard duly obliged, slipping past three players on the right-hand side of midfield before rifling home an unstoppable shot past the helpless Simon Mignolet in the Reds' net.
It was a typically brilliant moment from a man in the form of his life, having already scored five goals in Chelsea's first six Premier League matches this term.
Barkley offered up high praise for his colleague in the wake of the result at Anfield, as he told reporters: “Oh God, you see him do that every day in training so you’re not surprised when you see him do it in a game like that – but what a goal.
“He’s one of the best players in the world and he shows it.
“He’s been showing it for the last five or six years and he is establishing himself in the top three players in the world. At the minute, he’s probably the best player in the world, the way he is playing.”
Pressed further on whether Hazard can be placed above Lionel Messi and Cristiano Ronaldo, Barkley added: “Of course. They are probably a lot more selfish than Eden is. He is not a selfish player. He is happy getting two assists and the team winning. He is adding goals and he keeps improving … At the minute, he is the best player in the world, I believe.
“He is capable of producing magic at any moment in the game. He keeps defenders on the back foot and sometimes you see him attracting two or three players and that creates space for others, like myself, our other wingers and the strikers. When he gets closed down, he opens up space for others.”
Ronaldo, currently plying his trade in Serie A with Juventus, has shared the Ballon d'Or with Barcelona magician Messi equally over the last decade, but at the moment Chelsea's talismanic attacker is staking a strong claim to be considered in their league.
Under the leadership of Italian boss Maurizio Sarri, Hazard seems to be enjoying his football at club level more than ever before and the Blues are reaping the rewards after a strong start to the 2018-19 campaign.
Next up for Sarri's men is another showdown with Liverpool on Saturday, this time at Stamford Bridge, which could have a huge impact on the standings at the top of the table at this early stage of the season.