In a meeting between the Premier League's last two champions, it was the hosts who were by far the superior side as they raced into a two-goal advantage with a little over half an hour played in West London.
Leicester, who are the second defending champions to lose each of their first four away games after Blackburn Rovers two decades ago, did improve slightly in the second half but conceded a third late on through Victor Moses's strike.
The visitors' set-piece difficulties took just seven minutes to come to the forefront as the game's first corner kick led to the hosts' breakthrough goal.
City, who also slipped to an EFL Cup defeat to today's opponents just last month, were unable to put together any sort of attacking moves and it was Chelsea who were knocking on the door for a second.
Despite their positive passing moves from open play, the second nearly arrived from a dead-ball situation as David Luiz's free kick swerved through the air but back off the upright.
The Foxes did not heed the warning and they were indeed soon two behind after yet more comical defending, this time when Robert Huth and Luis Hernandez - in for his first start since the opening day - got in a muddle and the ball fell nicely for Hazard.
The Belgian did have a bit of fortune but he still had plenty to do, rounding the keeper and slotting over the line to put Chelsea well on their way to a comfortable home win.
Luiz had another chance to register his name on the scoresheet for the first time since returning to West London, but his latest free-kick attempt was parried by Schmeichel who was just happy to get something on the powerfully-struck shot.
Leicester had showed no signs of improvement for the remainder of the first half, though Claudio Ranieri - unbeaten against his former suitors last term - did have Islam Slimani and Riyad Mahrez to call upon from the bench.
Ranieri's decision to leave out two of his best attacking talents from the off was questionable, but the Foxes' attentions are now on furthering their Champions League aspirations as they close in on a place in the knockout stages.
There were early shouts for a penalty after the restart, with referee Andre Marriner adjudging that Pedro's shot hit Christian Fuchs's face and not his arm, while Moses also halted the run of Jeffrey Schlupp into the box moments later.
City, with the worst away record in the division at this early stage, certainly improved in the second period but were still unable to truly trouble their opponents in terms of shots on goal.
Chelsea really should have put the game out of the champions' reach just short of the hour when, at the end of a rare counter-attack, former Leicester man N'Golo Kante laid the ball on for Moses, who took on the shot first time which Schmeichel was equal to down to his right.
In what was proving to be a real end-to-end tussle in the second half, Leicester were next to come close to finding a way through after a cross from the right was diverted onto his own post by Luiz.
It proved to be a fine piece of defending from the Brazilian, who had Jamie Vardy waiting to pounce behind him, and it ensured City - without an away point since picking up a draw here on the final day of last season - just about remained in the game as the final 20 minutes approached.
Kante was to be denied a goal against the side he played a prominent role in helping to the title last term, seeing his shot blocked by Wes Morgan on the line, and Matic also had an effort pushed aside by Schmeichel 12 minutes from time.
There was still time for Chelsea to score a third, though, as substitute Nathaniel Chalobah produced a stunning flick on the edge of the area to play in Moses, who made no mistake against a Leicester side still seeking a first point on the road and unable to match last season's heroic defensive efforts.