In-form Willian had fired the visitors in front on 32 minutes before Lukaku restored parity shortly afterwards.
Both sides looked capable of snatching all three points, but it was substitute Lingard who had the decisive say when he nodded in Lukaku’s cross.
Alvaro Morata thought he had equalised for Chelsea late on but it was erroneously ruled out for offside, denying the Blues what, on balance, would have been a deserved point.
Here are three talking points as United reclaimed second spot and moved six points clear of Chelsea.
Lukaku makes a statement at long last
He was at the centre of a tug-of-war between United and Chelsea last summer before eventually joining the Red Devils to be reunited with Jose Mourinho, with whom he had worked at Stamford Bridge.
It is fair to say the Belgian’s not entirely justified the huge transfer fee, but this performance suggests the tide could be turning.
His goal, which settled United after a shaky start, was the first he had scored against a top-eight club this season and it could not have been more timely.
Emboldened by his strike, the 24-year-old looked back to his menacing best and, although Thibaut Courtois denied him a second of the afternoon, the Belgian played a key role in United’s winner.
His chipped ball to Lingard was inch-perfect, handing the England man an opportunity he couldn’t refuse to put the hosts in control.
This wasn’t a vintage United performance by any stretch, but it bore all the hallmarks of a Mourinho team.
Chelsea’s top-four hopes suffer a blow
He answered his critics to some degree as the Blues held mighty Barcelona to a draw in the Champions League in midweek.
This was another improved display from his charges, with no suggestion that they are not playing for their manager.
Willian’s goal was well deserved but their lead lasted only seven minutes.
Chelsea can feel aggrieved that Morata, who had earlier hit the woodwork, had a late effort ruled out for offside when he appeared to be level.
There are still 30 points to play so all is not lost for Chelsea, despite this setback.
But with competition so fierce, Conte knows his side face an uphill climb to finish in a Champions League spot.
Super-sub Lingard presses his case
While Lukaku had struggled to have an impact in the crunch games, the same cannot be said about Lingard.
He was in sparkling form earlier this season, scoring six goals in a nine-match spell over the festive period.
Although that form tailed off to an extent, the 25-year-old reminded Mourinho of his ability to make something happen.
Ten minutes after coming on for Anthony Martial, Lingard was at the centre of the celebrations when he converted Lukaku’s cross.
Despite having a peripheral role at times, this was his 13th goal in all competitions for United this season.
England boss Gareth Southgate is a known admirer of Lingard’s and, with World Cup selection on the horizon, the United academy product will be hoping to get as much game-time as possible in order to book his place on the plane to Russia.
After this telling cameo against Chelsea, Mourinho may have a hard time leaving him out of the starting XI.