Jose Mourinho’s third Premier League title and Chelsea’s first for five years could be just 11 days away after Hazard’s 38th-minute strike sent the Blues 10 points clear of second-placed Arsenal.
Mourinho has taken a game-by-game approach to the season and will refuse to get ahead of himself, but win at the Emirates Stadium on Sunday week and Chelsea could be crowned champions at Leicester three days later.
Arsenal would have five games to play, but the Blues would have an unassailable 16-point lead and clinch the self-proclaimed Special One’s third English championship following his successes in 2005 and 2006.
United, who began the day eight points behind, dominated the opening period, but their only chance of note saw Wayne Rooney shoot narrowly wide.
Hazard then showed why he is favourite for the PFA Player of the Year prize, netting his 18th goal of the season on the counter-attack following Oscar’s fine flick.
Leicester climbed off the bottom of the Barclays Premier League as a 2-0 home win over Swansea gave them a third successive victory.
Burnley’s survival hopes suffered a blow in a controversial 1-0 defeat at Everton, Roberto Martinez’s Toffees now unbeaten in five league games.
Referee Mike Jones awarded a contentious 10th-minute penalty to Everton after Aaron Lennon had appeared to be fouled outside the area by David Jones, but Tom Heaton saved Ross Barkley’s spot-kick.
Kevin Mirallas gave Everton a 29th-minute lead from James McCarthy’s cross before Burnley were reduced to 10 men on the stroke of half-time when Ashley Barnes was sent off for two bookable offences.
Tony Pulis enjoyed a happy return to Crystal Palace as his West Brom side eased their relegation worries by winning 2-0 at Selhurst Park.
Stoke beat Southampton 2-1 at the Britannia Stadium as the Potters claimed their first top-flight victory over Saints in 15 matches.