Alvaro Morata's early second-half header condemned United to another defeat at Stamford Bridge and a second successive away league loss.
Morata headed home the decisive goal from Cesar Azpilicueta's cross as the Blues responded from their midweek mauling in Roma to move one point behind us in the table.
United certainly had their moments and almost salvaged a point in a spirited late rally, but the long winless run in west London now stretches into a sixth year.
Many predicted a tight and cagey affair, but, on Bonfire Night, the contest quickly exploded and sparked into life as both sides started strongly.
The fit-again N'golo Kante gave David de Gea an early sighter, before Phil Jones bizarre own goal was ruled out after a tussle with Morata from a Marcos Alonso cross.
Marcus Rashford spurned United's best opening with a header from close range, and - at the other end- Tiemoue Bakayoko should have done better when well placed.
Two former Blues then linked up as Nemanja Matic played in Romelu Lukaku, but Thibaut Courtois did well and pushed away the Belgian's snap shot.
De Gea had to be alert to a rocket from Hazard, while Cesc Fabregas headed into the side netting on the follow-up as Chelsea started to take control.
The impressive Andreas Christensen, drafted in to replaced David Luiz, went close with another header from a corner shortly before the break.
The second half started as the first had ended, with Antonio Conte's side carving out most of the openings.
Ten minutes after the interval, Chelsea moved ahead.
Hazard swept a volley straight at de Gea, but from their next attack, Azpilicueta picked out Morata and he drifted into space to power home a superb header into the top corner.
The returning Marouane Fellaini was introduced along with super sub Anthony Martial as United attempted to turn the tide and put to an end the miserable run of form at the Bridge.
In fact, it was Chelsea who went close again through Bakayoko, who fired wide, and Hazard, who was denied by a smart save from de Gea on 72 minutes.
The Reds mounted a late surge, and had three good chances to snatch a late equaliser in the closing stages.
Rashford flashed a shot narrowly over the bar from distance, Martial fired wide and Fellaini had an excellent effort tipped away by Courtois soon afterwards.
But that proved to be the Reds last opportunity as Chelsea held firm to leave United with a familiar sense of frustration at our biggest bogey ground.
Overall team performance: 6/10
United Faithful Man of the Match: Antonio Valencia. Solid and the source of United's main supply line