Hazard put Chelsea ahead with a low, angled shot, before Marcos Alonso added a second when he slotted through Maarten Stekelenburg's legs.
Diego Costa made it 3-0 just before half-time, and Hazard scored the pick of the goals after the break.
Pedro put the gloss on the result when he tapped into an empty net.
Everton spent the majority of the game penned in their own half and did not manage a shot on target in the entire 90 minutes as Chelsea produced a ruthless and dominant performance.
Many of the visiting supporters left Stamford Bridge well before the final whistle. Those that remained applauded Chelsea off the pitch, with the biggest ovation of all from the home fans reserved for Hazard, who capped a brilliant display with two superb goals.
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In an attempt to stifle the 3-4-3 system that had earned Antonio Conte's side four consecutive Premier League wins before this match, Everton manager Ronald Koeman reverted to three men at the back.
However, the tactical ploy proved ineffective as the Dutchman's side were outpassed and outclassed by Conte's men in a mesmerising first-half display.
Confidence has been high among Chelsea's players since their 4-0 demolition of Manchester United last month, and the swagger with which they dismantled Everton will only further fuel talk of a title challenge.
In the five games since the formation change, Conte's side have scored 16 goals and conceded none.
Chelsea look a completely different team from the sluggish outfit that struggled under Jose Mourinho last season, and this performance was a real statement of intent.
Everton striker Romelu Lukaku would have been desperate to impress against former club Chelsea, but the Belgium international was a subdued presence.
Luakaku, who joined Everton from Chelsea for a club record £28m in July 2014, was barely able to get on the ball in the final third as Chelsea dominated.
Despite being paired with Yannick Bolasie, he was deprived of service, and spent large parts of the game chasing lost causes.
The 23-year-old has now played five Premier League matches for the Toffees against his former club, but is yet to score.
If Lukaku endured a frustrating game, the opposite was true for compatriot Hazard, who has rediscovered his joie de vivre and scored for a fourth consecutive league game.
Chelsea striker Diego Costa may have had a hand in more goals than any other Premier League player, with nine goals and three assists, but it is Hazard who has supporters on their feet whenever he is on the ball.
The effortless manner with which he glided past the dazed yellow shirts of Everton's defence for his two goals was breathtaking.
Conte claimed the 25-year-old forward is on the right track to becoming one of the world's best players, and on this evidence that is no exaggeration.
BBC Match Of The Day pundit Ian Wright said: "Eden Hazard was world class against Everton. I think Ronald Koeman picked the wrong day to pick three at the back."
Chelsea boss Antonio Conte: "It was a great game, a good performance. It is important for confidence to be top of the league. We have to continue as Everton is now in the past.
"The players deserve this because they show me great commitment and I can tell they are working very hard. The team has more balance defensively, but we don't lose our offensive situation. We are creating more chances to score goals.
"Eden Hazard played an impressive game. We all know he is a talented player. I see he is working a lot for the team and his team-mates are very happy for this. He must continue - he is showing his talent in every game."
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Everton manager Ronald Koeman: "The difference was too big between Chelsea and Everton. The one positive thing is it is only three points.
"This system is very difficult to play against and really the Chelsea manager has brought a winning mentality to the players. They are hungry and they will fight for the title for sure.
"I expected more from my team. It was a big difference in every aspect.  It was not about the system - the difference was the mentality to win the game. With five defenders we control it, after 2-0 it was over."
After the international break, Chelsea face Middlesbrough at the Riverside Stadium on Sunday, 20 November with a 16:00 GMT kick-off, while a day earlier Everton have a 15:00 GMT home fixture against struggling Swansea.
Match ends, Chelsea 5, Everton 0.
Second Half ends, Chelsea 5, Everton 0.
Foul by John Terry (Chelsea).
Romelu Lukaku (Everton) wins a free kick in the attacking half.
Marcos Alonso (Chelsea) wins a free kick in the defensive half.
Foul by Tom Davies (Everton).
Offside, Chelsea. John Terry tries a through ball, but Diego Costa is caught offside.
Attempt saved. Victor Moses (Chelsea) left footed shot from outside the box is saved in the bottom right corner. Assisted by Diego Costa.
Foul by N'Golo Kanté (Chelsea).
Tom Davies (Everton) wins a free kick in the attacking half.
Substitution, Chelsea. John Terry replaces Gary Cahill.
Victor Moses (Chelsea) wins a free kick in the defensive half.
Foul by Kevin Mirallas (Everton).
Attempt blocked. Michy Batshuayi (Chelsea) right footed shot from outside the box is blocked.
Attempt blocked. N'Golo Kanté (Chelsea) right footed shot from outside the box is blocked. Assisted by Diego Costa.
Corner,  Chelsea. Conceded by Maarten Stekelenburg.
Attempt saved. David Luiz (Chelsea) right footed shot from the right side of the box is saved in the top centre of the goal. Assisted by Oscar with a cross.
Substitution, Chelsea. Michy Batshuayi replaces Eden Hazard.
Corner,  Chelsea. Conceded by Ashley Williams.
Attempt blocked. Diego Costa (Chelsea) left footed shot from the left side of the box is blocked. Assisted by Oscar with a through ball.
Attempt blocked. Diego Costa (Chelsea) right footed shot from the right side of the box is blocked.
Marcos Alonso (Chelsea) wins a free kick on the left wing.
Foul by Ross Barkley (Everton).
Attempt missed. Kevin Mirallas (Everton) header from a difficult angle on the left is just a bit too high. Assisted by Ross Barkley with a cross following a corner.
Substitution, Chelsea. Oscar replaces Pedro.
Corner,  Everton. Conceded by Victor Moses.
Substitution, Everton. Tom Davies replaces Gareth Barry.
Goal!  Chelsea 5, Everton 0. Pedro (Chelsea) left footed shot from the centre of the box to the centre of the goal.
Attempt saved. Eden Hazard (Chelsea) right footed shot from the left side of the box is saved in the bottom right corner. Assisted by Diego Costa.
Gareth Barry (Everton) is shown the yellow card for a bad foul.
Pedro (Chelsea) wins a free kick in the attacking half.
Foul by Gareth Barry (Everton).
Attempt blocked. Pedro (Chelsea) left footed shot from outside the box is blocked. Assisted by Marcos Alonso.
Attempt saved. Diego Costa (Chelsea) right footed shot from the centre of the box is saved in the centre of the goal. Assisted by Marcos Alonso.
Substitution, Everton. Aaron Lennon replaces Yannick Bolasie.
Diego Costa (Chelsea) wins a free kick in the attacking half.
Foul by Gareth Barry (Everton).
Goal!  Chelsea 4, Everton 0. Eden Hazard (Chelsea) left footed shot from the right side of the box to the bottom right corner. Assisted by Pedro.
Attempt blocked. Victor Moses (Chelsea) left footed shot from the centre of the box is blocked. Assisted by Nemanja Matic.
David Luiz (Chelsea) wins a free kick in the defensive half.
Eden Hazard scored twice as Chelsea climbed to the top of the Premier League for the first time since August with a stylish victory over Everton.