Premier League review: Chelsea move step closer to title with win over Man City
Antonio Conte's side showed resilience in responding from their surprise loss to Crystal Palace and the gap at the top remained seven points as second-placed Tottenham came from behind to win at Swansea.
Goalkeeping errors contributed to the opening goals as Hazard shot through Willy Caballero and Thibaut Courtois gifted City an equaliser, scored by Sergio Aguero.
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Hide AdHazard saw a penalty saved by Caballero, but tucked in the follow-up to give Chelsea a 2-1 half-time lead which they would not relinquish.
City poured forwards time and again in the second half and John Stones missed from three yards in stoppage time.
Tottenham kept their title ambitions alive by staging an extraordinary late show at relegation-threatened Swansea.
Swansea led from Spurs old boy Wayne Routledge's 11th-minute goal through to the 88th minute as it looked like Mauricio Pochettino's men would slip 10 points behind Chelsea.
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Hide AdBut Dele Alli equalised with his 15th league goal of the season before Son Heung-min and Christian Eriksen struck in added time to complete a remarkable 3-1 victory - their fifth successive league win.
It could prove a costly defeat for Swansea who drop into the relegation zone with seven games left to play.
That fall came about because Hull climbed out of the bottom three for the first time since October and pushed Middlesbrough closer towards relegation with a thrilling 4-2 win at the KCOM Stadium.
Oumar Niasse and Abel Hernandez gave Hull a two-goal cushion after team-mate Lazar Markovic had cancelled out Alvaro Negredo's early opener for Middlesbrough in a breathtaking first 45 minutes.
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Hide AdBoro hit back in first-half stoppage-time through Marten de Roon's controversial header before Harry Maguire headed Hull's fourth midway through the second period.
Victory was the Tigers' fifth in six home league games and lifted them two points above Swansea, while Boro, without a league win since December 17, appear destined for a return to the Sky Bet Championship.
Middlesbrough played their full part in a pulsating encounter, but are now seven points adrift of safety with eight games remaining.
Arsenal returned to winning ways with a solid 3-0 victory over West Ham as a fifth straight defeat plunged Slaven Bilic's visitors deeper into the fight for Premier League survival.
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Hide AdBoth sides went into the London derby in dire form but it was the Gunners who addressed that and achieved their first league win since February 11.
Mesut Ozil marked his 150th Arsenal appearance with a tame opening goal before laying on the second for Theo Walcott. Olivier Giroud came off the bench to score the goal of the night.
Liverpool let a lead slip away late on to draw 2-2 against Bournemouth and miss the chance to strengthen their grip on third place.
Goals from Philippe Coutinho and Divock Origi appeared to have put the hosts on course to open up a six-point gap on fourth-placed Manchester City.
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Hide AdHowever, Josh King struck in the 87th minute, to follow Benik Afobe's early opener, as Bournemouth earned a point.
Maya Yoshida and James Ward-Prowse spared Shane Long's blushes as Southampton hit two goals in as many minutes to sink Crystal Palace 3-1 at St Mary's.
Republic of Ireland striker Long spurned a trio of chances and Saints were almost made to pay for that wastefulness, until Yoshida came to the rescue.
The Japan defender's tap-in seven minutes from time turned the game, after Christian Benteke and Nathan Redmond had traded first-half goals.