The Spaniard returned the ball to advancing Hazard, who went past three players, cut inside and sent a shot across goalkeeper Simon Mignolet and into the net.
He has hit Lionel Messi and Cristiano Ronaldo level since the start of the World Cup, and is finally getting recognition as one of, if not the, best in the world.
The Reds exited the League Cup on Wednesday night, as they suffered their first defeat at Anfield since January.
With both teams unbeaten so far this season in the Premier League and European action, plus Liverpool winning all seven of their games an Chelsea winning six, this should be a fine game for the neutral.
But instead it was Hazard who showed his class to strike the victor as he danced past five Liverpool challenges before crashing a rising shot into the far corner for his sixth goal of the season.
"I've seen him day in, day out for the last five/six years and he's a top, top player and he will only get better as well".
Petr Cech reveals what went wrong with Arsenal under Arsene Wenger
Former Liverpool defender Jim Beglin and Don Hutchison have suggested that Marco Silva's Everton need to sign a striker. Everton had created a fistful of good chances in the first half only to run into Petr Cech in inspired form.
Six minutes later, a moment of individual magic from Hazard put Chelsea ahead.
"This result will give us more confidence because we drew with West Ham four days ago". While Liverpool have the upper hand in the league the Carabao Cup match in midweek has given Chelsea the impetus.
"I expect to see goals in what promises to be a cracker". The Belgian may not have his goal scoring numbers up like Neymar, but he certainly makes up for that by baiting himself for others to get on the score sheet. Put Hazard in any team and he will thrive, the same can not be said for Neymar.
Liverpool, though, will quickly have a chance for revenge as they head to Chelsea protecting a ideal Premier League record for a blockbuster Stamford Bridge clash on Saturday.
The German will have been encouraged by Shaqiri's impact and may feel he can use him in Saturday's trip to Stamford Bridge.