Hazard opened the scoring and restored Chelsea's lead 10 minutes before the break after Sergio Aguero levelled for the visitors, converting at the second attempt after Willy Caballero saved his tame penalty.
City pressed for a leveller throughout the second half but Chelsea held out for the ideal response to Saturday's shock loss to Crystal Palace, with the gap at the summit remaining at seven points with eight games to play after nearest rivals Tottenham came back for a dramatic late 3-1 win over Swansea City.
It is a race Pep Guardiola will now watch from a distance, with his captain Vincent Kompany's successful return from his latest lengthy absence providing a positive for the battle ahead to secure Champions League qualification.
City – who saw John Stones miss a glorious chance in stoppage time – have now gone four Premier League games without a win and are fourth, four points ahead of Manchester United and Arsenal having played a game more than both.
If at first you don't succeed... pic.twitter.com/Y4EoewZg8r— Chelsea FC (@ChelseaFC) April 5, 2017
Kurt Zouma made his first Premier League start for 14 months, seeing Cesar Azpilicueta revert to right wing-back and the Spain international combined well with compatriot Pedro to set up Chelsea's 10th-minute opener.
Azpilicueta's pull-back found Hazard in the area and, even allowing for a slight deflection off Kompany, the Belgium star's shot should have been better dealt with by flapping City goalkeeper Caballero.
The goalscorer glided down the City right midway through the half and spun in field to tee up Cesc Fabregas, with Gael Clichy deflecting the midfielder's attempt onto the roof of his own net.
In the 26th minute, Courtois was the goalkeeper to be embarrassed, marking his 100th Chelsea appearance with a dreadful clearance straight to David Silva.
He saved the initial shot but Aguero – booed throughout by the home fans following his red card for an ugly lunge on David Luiz during December's reverse fixture – was on hand to tap in his 27th of the season.
GET IN!!! pic.twitter.com/7j8rGHQJGX— Manchester City (@ManCity) April 5, 2017
Courtois partially atoned for his error two minutes later when Silva split Chelsea with a wonderful throughball and he dashed from his line to deny Leroy Sane.
The hosts appeared to be wobbling but ventured forward in the 34th minute and Pedro's sidestep was too deft for Fernandinho, who clumsily felled the former Barcelona man. Hazard's penalty was poor as Caballero saved to his left, but the rebound fell kindly.
Zouma made way at the break and Kompany almost capitalised on Chelsea's reshuffled backline early in the second period, looping a header against the top of the crossbar from Kevin De Bruyne's deep free-kick.
From a 51st-minute set-piece opportunity, Fabian Delph – another man making his first Premier League start of the season – worked the ball back into the Chelsea box and Fernandinho, adjudged onside, shanked a volley wastefully over.
Silva poked and prodded inventively at the Chelsea defence all evening and Stones should have done better than planting his 65th-minute corner straight at Courtois.
Hazard orchestrated a 76th-minute counter-attack that deserved to end with him claiming the matchball as opposed to smashing beyond the crossbar, although an apparently flagging City twice went close in stoppage time.
Courtois saved when substitute Nolito picked out Aguero with a brilliant raking ball and the goalkeeper and his team-mates breathed a sigh of relief from the resulting corner, when Stones lifted inexplicably over the bar to leave Chelsea's advantage at the top intact.
Key Opta Facts:
- Eden Hazard is the first Chelsea player to score home and away against Manchester City in the Premier League since Salomon Kalou in 2007-08.
- Hazard now has 10 Premier League goals at Stamford Bridge this season - more than any other player.
- Sergio Aguero has now scored nine goals in his last nine appearances for Manchester City in all competitions.
- Aguero has scored five goals at Stamford Bridge as an away player in the Premier League - the only player with more is Robin van Persie (6), while Craig Bellamy also has five.
- Pep Guardiola has suffered six league defeats as Manchester City boss this season - his highest tally in a single league season as a manager.