The Red Devils produced one of their better displays under Jose Mourinho, who finally got to celebrate getting one over on his former employers at the third time of asking this term.
Marcus Rashford got the ball rolling for United early on and Ander Herrera added a second shortly after the second-half restart, as the hosts extended their unbeaten league streak to 22 games - the best such run in Europe's five major leagues.
United are now four points adrift of fourth-placed Manchester City in the table with a game in hand to play, while Chelsea's advantage on closest challengers Tottenham Hotspur at the top remains at a slender four points.
Chelsea were forced into making a late change to their starting lineup, as illness victim Marcos Alonso was replaced in the backline by Kurt Zouma, meaning a switch of positions for the versatile Cesar Azpilicueta.
Whether down to that last-minute tinkering or United's surprise choice of tactics - Mourinho going with a three-man forward line after leaving out Zlatan Ibrahimovic - the Blues failed to get going at all in the first half.
The Red Devils were ahead through their fastest league goal of the Mourinho era, thanks to a simple through-ball from Herrera - who handled the ball in the build-up - for Rashford to peel off David Luiz and tuck home.
Young sent one shot-cross from the left agonisingly close to the far corner, while also skying a shot from the edge of the area with the final attempt of a first half dominated by his side.
Gary Cahill endured an awkward moment shortly beforehand when glancing Rashford's cross onto the roof of his own net, though for all of the Red Devils' possession they only managed the one shot on stand-in Blues stopper Asmir Begovic's goal in the opening 45.
The omens did not look great for Chelsea at the midway stage, as they had lost four of the previous five matches they had trailed at the break, with their single shot on target in the first half - their lowest of the season so far - not providing much hope of a comeback.
A first Premier League goal in 14 months for Herrera made Chelsea's task all the more difficult just four minutes into the second period, firing a loose ball past a wrong-footed Begovic with the aid of a big deflection off Zouma.
Lingard was riding on the wave of joyous home fans when curling one over moments later, and half of Old Trafford thought that Rashford had added a third when thumping a powerful drive into the side-netting.
A fine Rashford display was almost capped with a second goal when somehow keeping hold of the ball under pressure from Luiz and Zouma, before guiding a low shot on target for Begovic to keep out from the final meaningful act of the match.