Marcus Rashford gave the hosts the lead from the penalty spot in the first half, but the match was hanging in the balance until a 16-minute blitz which saw Frank Lampard's side blown away in his first game in charge of Chelsea.
Two goals in the space of 95 seconds - one from Anthony Martial and then a second for Rashford - essentially put the game to bed before Daniel James added the cherry on top with a debut strike off the bench.
Neither manager will get too carried away with the relatively flattering size of the scoreline, although for United it was the type of dynamic and exciting performance the fans have been crying out for in recent years.
Ole Gunnar Solskjaer handed debuts to Harry Maguire and Aaron Wan-Bissaka in what was the youngest starting XI of any team on the opening weekend, while Chelsea's side also had a youthful look with Mason Mount and Tammy Abraham included.
The latter almost made a dream start to the match too as he got the better of Rashford on the edge of the box before swivelling and powering a well-struck shot past David de Gea, only to see it crash against the post.
Chelsea settled much the quicker of the two sides, but United were almost gifted an opener when Kurt Zouma gave possession away cheaply on the edge of his own box and Martial saw his subsequent effort saved by Kepa Arrizabalaga.
It was the first of a few incidents where Zouma looked shaky during the first half, but the rest of his Chelsea teammates kept Lampard's side on top during the opening exchanges and Mount forced a first save from De Gea with a powerful long-range strike.
Despite a sluggish start it was United who took the lead, though, with Zouma again the guilty party from Chelsea's point of view as he brought Rashford down inside the area with an ill-judged sliding tackle.
Rashford got up to take the penalty himself after a brief check with VAR and put his spot kick beyond the dive of Kepa for United's first goal of the season.
While the goal itself came against the run of play, it also served to spark United into life and the Red Devils had the better of the following 15 minutes without creating too much to worry Kepa.
Chelsea began to grow into the game again towards the end of the half, though, and Ross Barkley flashed one low drive narrowly wide before forcing De Gea into a smart save with his feet.
De Gea was beaten moments later when Wan-Bissaka could only clear a cross as far as Emerson Palmieri, but once again the woodwork came to United's rescue as the full-back's powerful strike clattered against the angle of post and crossbar.
Chelsea were also the team that looked most like scoring at the start of the second half with Pedro curling an effort over before De Gea was needed to parry a powerful Emerson strike away from goal.
United have never lost a Premier League game at Old Trafford when leading at half time, though, and they kept that remarkable record going with a quickfire double which took the game away from Chelsea.
Having only managed one win against top-six opposition throughout the whole of last season, United then ensured they would equal that tally on the opening weekend of this term with a third goal just 95 seconds later.
Pogba split a disorganised Chelsea defence with a sublime pass over the top for Rashford, who only had the keeper to beat and made no mistake with his finish.
With the result wrapped up United could focus on keeping a clean sheet - something they managed just twice at home in the league in 2018-19 - and Emerson was the biggest threat to that for Chelsea as he forced De Gea into another save.
The hosts got their fourth goal with nine minutes remaining to add insult to injury as again Chelsea were unable to cope with their pace on the counter-attack, with Pogba leading the charge once more.
The French midfielder, who had been heavily linked with a move away during the transfer window, carried the ball from deep inside his own half before giving it to James, whose shot deflected in off Emerson to give him a debut goal just seven minutes after he was brought off the bench.
Mount and Emerson provided late threats of a consolation for Chelsea, but United held on for their first Premier League clean sheet since February 24 to make it a perfect start to their campaign.
Lampard, meanwhile, becomes the first Chelsea boss since Avram Grant to lose his first match in charge of the club and must now pick his side up ahead of Wednesday's UEFA Super Cup clash with Liverpool in Istanbul.
MAN UTD (4-2-3-1): De Gea; Wan-Bissaka, Maguire, Lindelof, Shaw; McTominay, Pogba; Lingard (Mata 86'), Pereira (James 74'), Rashford (Greenwood 86'); Martial
CHELSEA (4-2-3-1): Kepa; Azpilicueta, Christensen, Zouma, Emerson; Jorginho (Kante 73'), Kovacic; Pedro, Mount, Barkley (Pulisic 58'); Abraham (Giroud 66')