Marcus Rashford scored twice, either side of a close-range effort from Anthony Martial, who had been given the number nine shirt back following the sale of Romelu Lukaku to Inter Milan.
Substitute Daniel James completed the scoring with a goal on his debut nine minutes from time.
The final scoreline was harsh on the visitors, who were the better side before the break and hit the frame of the goal through Tammy Abraham and Emerson, but still suffered their worst ever opening-day defeat in 104 league seasons.
The ecstatic home supporters did not care about that though, as the negativity of a difficult summer was swept away by their best result against Chelsea since they beat them by the same score in the 1994 FA Cup final.
United had to pay Leicester £80m - and make Harry Maguire the most expensive defender ever - to land manager Ole Gunnar Solskjaer's number one summer transfer target.
Maguire's England team-mate Rashford may grab the plaudits with his brace but the Yorkshireman's authoritative performance underlined why his new boss wanted him above getting the big name midfield or striking reinforcements so many United fans have demanded on social media.
His calmness under pressure helped ensure that when the home side looked shaky in the first half they did not add to their concerns with self-inflicted mistakes.
Maguire was happy to keep it simple in possession and push the ball on to Paul Pogba when he could, and had the awareness to spot team-mates in trouble, something former United boss Jose Mourinho rather churlishly said on TV might be frequently needed in the case of Luke Shaw.
The game was still in the balance when Maguire stepped up to challenge Abraham on the edge of the United box. Maguire calmly took possession, leaving Abraham on the floor in the process, and strode away, setting in motion the attack that ended with Martial bundling home.
Risky strategy
Lampard went for an early morning run around Old Trafford to prepare for his Premier League debut as Chelsea manager.
The Blues' record goal-scorer has made some bold decisions already, despite being barely a month into his new job.
He has picked seven home-grown players in his senior squad: the four in action against United - Abraham, Mason Mount, Andreas Christensen and Fikayo Tomori - the currently injured duo of Ruben Loftus-Cheek and Callum Hudson-Odoi, and promising defender Reece James.
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This was Chelsea's heaviest ever opening-day league defeat in what is their 104th league season
It is an unprecedented number for the Roman Abramovich era. But, while it is the philosophy of promoting youth from within that Chelsea's fans have wanted, it comes with risk.
For every powerful fourth-minute shot from Abraham that thunders off the inside of a post, there is the moment Mount had when, presented with a shooting opportunity from an angle on the right of the United box, the 20-year-old elected for a cut-back, which ran disappointingly through for new United defender Aaron Wan-Bissaka.
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