Perhaps fearful of losing their third straight game to Chelsea this season and, indeed off the back of fierce criticism from Jose Mourinho three days earlier, United were superb going forward as they took just seven minutes to take the lead against Antonio Conte's Chelsea.
The opener came in controversial circumstances, however, when Ander Herrera appeared to control the ball with his arm before superbly setting up Marcus Rashford, who fired past Asmir Begovic.
Herrera then got on the scoresheet himself when, just four minutes into the second half, the Spaniard latched onto a loose ball in the area before seeing his low effort deflect off Kurt Zouma and into the back of the net.
The hosts could have had more against a lucklustre Chelsea side but secured a 2-0 win that takes them to within four points of fourth-placed Manchester City while Chelsea now lead second-placed Tottenham by the same margin.
Blues boss Conte has enjoyed a season in which many of his first-team stars haven't had major injuries to contend with although, on Sunday, the Italian was forced to go to Old Trafford without first-choice goalkeeper Thibaut Courtois, who was ruled out with an ankle injury.
While Courtois - who has been solid for the leaders this season - would have felt like a huge loss for Conte, the Italian would have been even more frustrated when Marcos Alonso was ruled out of the game late on through illness.
It meant Conte having to reshuffle his back line to include Kurt Zouma in his three-man defence while Cesar Azpilicueta was pushed onto the left flank as a wing-back.
But the changes ended up working in United's favour with Rashford proving a nuisance for Azpilicueta and, indeed, all of Chelsea's defence early on.
Perhaps heeding Mourinho's criticism of United's forwards on Thursday - when the Portuguese expressed his frustration at his attackers being sloppy in the 1-1 Europa League draw against Anderlecht - Rashford was sharp and clinical against Chelsea.
And he was rewarded for his fast start when in only the seventh minute, Herrera intercepted Nemanja Matic's pass with his arm before threading the ball to Rashford, who outpaced David Luiz to coolly fire past Begovic.
While Herrera's pass was undoubtedly superb, the Chelsea players were left fuming with the midfielder's handball in the build-up to the opener although referee Bobby Madley appeared to miss the incident altogether.
United continued on in the same vein, however, and pushed men forward to hand Chelsea's defence a lot of work in the first half.
Indeed, Ashley Young could have doubled United's advantage just nine minutes later when he drove the ball wide of the post before Rashford forced Begovic into a one-handed save soon after.
The 19-year-old was one of the hosts' best players and, in an attempt to stop the striker's impact on the game, Conte moved Azpilicueta from the left wing to the right, with Victor Moses being tasked with the aim of trying to contain Rashford.
It worked to an extent while at the other end of the pitch, Chelsea striker Diego Costa was booked for a late challenge on Paul Pogba.
Costa, who still hasn't scored in the Premier League since 6 March, appeared frustrated throughout but was involved in Chelsea's first chance at goal just before the break when he delivered a long-range effort that flew wide.
If Conte thought his team talk at the break would inspire his players onto a reaction in the second period then the Chelsea manager would have been thoroughly disappointed.
Within just four minutes of the re-start United had the ball in the back of Chelsea's goal again after Zouma dispossessed Young inside the box, but saw the ball fall to Herrera instead.
The midfielder didn't hesitate to go for goal and he sent a low effort towards the net, which deflected off Zouma and past Begovic to make it 2-0 to United.
Lingard could have made it three but fired high moments later before Conte sent on Cesc Fabregas and Willian. The duo injected more creativity and pace into the visitors' attack, with Pedro seeing his effort fly just over the bar in the 64th minute.
But United defended well to contain all of the Blues' attempts at their goal and went on to beat Chelsea 2-0 and blow the Premier League title race wide open