Belgium international Hazard found a neat finish in the 38th minute to grab his 18th goal in all competitions this season after Chelsea spent much of the opening period on the back foot.
United continued to dictate possession after the break but the hosts, who now have 76 points with six games remaining, defended stoically and stretched their advantage over second-placed Arsenal, who they visit next weekend.
United are a further point back in third, four clear of rivals Manchester City who host West Ham United on Sunday.
Louis van Gaal’s side, having won six successive league matches, arrived in west London full of confidence and with a realistic chance of leapfrogging Arsenal into second.
Without their metronomic midfield anchor Michael Carrick and the underrated Daley Blind, Wayne Rooney was deployed in a deeper role and almost opened the scoring in the fourth minute but his curling effort flashed past the post.
Alongside Rooney, Ander Herrera controlled possession, setting the tempo for the visitors, and was the catalyst for many of United’s attacks in an impressive opening 30 minutes.
For all their possession and endeavour, though, United failed to breach Chelsea’s watertight defence and were made to pay by a slick counter-attack in the 38th minute.
United striker Radamel Falcao was dispossessed in midfield before Oscar flicked the ball into the path of Hazard who burst into the area and slotted through the legs of David De Gea.
Hazard could have added a second goal shortly after the break but his flick hit the woodwork after Didier Drogba’s deflected shot looped over De Gea and into his path.
United defender Paddy McNair drew a save from Thibaut Courtois and Falcao also fired against the woodwork as United’s pressure intensified.
The hosts, however, were equal to the task and it will take a mighty capitulation for Chelsea, unbeaten in the league since Jan. 1, not to win a fourth Premier League title.
(Editing by Ken Ferris)
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