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.
The strike, seven minutes before half-time, shifted the momentum of the contest in Chelsea's favour.
Juan Mata has been influential in recent weeks, but he was unable to inspire United on his first return to his old stomping ground.
Kurt Zouma, meanwhile, fully justified his inclusion in midfield in combating the considerable threat of Marouane Fellaini.
United had reason to feel aggrieved when Ander Herrera was booked for diving when tripped by Gary Cahill in stoppage time.
Referee Mike Dean ignored United's penalty appeals and Mourinho and Chelsea were able to celebrate a significant triumph.
Rooney started in central midfield to accommodate Radamel Falcao as one of three changes for injury-depleted United, while Chelsea made two changes following the win at QPR, with Zouma and Oscar coming in
Loic Remy was unable to return from his calf problem and Diego Costa (hamstring) is at least a week away from a comeback, so Didier Drogba continued up front for the Blues.
With Herrera dictating play in holding midfield and Luke Shaw racing up the left, United penned Chelsea back in their own half and appeared not to miss Michael Carrick (calf) and Daley Blind (ankle).
It was Chelsea who appeared to miss their absentees most early on and the visiting fans and goalkeeper David de Gea thought Rooney had scored from Shaw's cut-back, but the ball veered narrowly wide before rippling the net from behind.
United's start was strong enough for their central defenders to wander forward, with Chris Smalling strolling into midfield before a wild pass and Paddy McNair - in for Phil Jones (ankle) - forcing a corner from his shot.
Chelsea were playing on the counter, but Drogba's pass towards Hazard, who was in a promising position, was intercepted.
De Gea met a hopeful cross with his fist on the edge of the area, with the goalkeeper given the benefit of the doubt.
The next contentious decision went Chelsea's way as John Terry tackled Falcao, who had his back to goal.
The ball went to Cesc Fabregas down the left and the masked playmaker fed Oscar, who exquisitely back-heeled the ball to Hazard.
The Belgium forward surged into the left side of the area before slotting the ball under De Gea.
United boss Louis van Gaal made his displeasure known to fourth official Craig Pawson, but his complaints fell on deaf ears and Chelsea were transformed from submissive to dominant, epitomised by another physical challenge from Terry on Falcao.
Chelsea and Hazard came close to a second when Herrera gifted the ball to Nemanja Matic.
Matic's through ball released Drogba, who held off Smalling to get a shot away which De Gea saved.
Hazard tried to acrobatically flick it in from an acute angle, but it hit the post.
Another McNair shot from 25 yards was deflected and saved by Thibaut Courtois and Mata next went close from Shaw's cross.
Cahill blocked from Falcao, who had fired just wide, before United made changes in attack, with Mata and Ashley Young replaced by Adnan Januzaj and Angel di Maria.
Falcao got behind Zouma to latch on to Shaw's pass and struck the outside of the post.
Herrera then went over just inside the box, with Cahill complaining.
Rooney was among the United players to express his displeasure towards Dean, but the official ruled in Chelsea's favour as the Blues moved within reach of the title.
Source : PA
Source: PA