Goals from Micah Hamilton and Will Dickson put the young Blues firmly in control before United's Sonny Aljofree was sent off for hauling down Oscar Bobb.
Dickson got his second shortly afterwards to give City a commanding lead before the half-time break.
Bobb tapped home the fourth before late strikes from Kian Breckin and Jaden Heskey rounded off the scoring in a dominant display from Brian Barry-Murphy's side.
In front of a packed-out stand at the Academy Stadium, City came flying out of the blocks right from the first whistle.
The Blues nearly took the lead in the opening two minutes, with Bobb firing wide after working some space for himself inside the area.
But we would not have to wait long until we got ourselves ahead, the breakthrough coming in the seventh minute as Mebude got to the byline, and had time to pick out the on-rushing Hamilton who scored on his first start back in the EDS.
Seven minutes later, the lead was doubled and once again it came via Mebude, sprinting onto a well-placed through ball before crossing into the area. United defender Bjorn Hardley got his foot to it but could only poke it into the path of Dickson, leaving the striker with the simplest of finishes.
What was turning into an uphill climb for United soon turned into a mountain when, with just 21 minutes played, Sonny Aljofree lost the ball with a poor touch before dragging down Bobb who was sprinting through on goal, leaving the referee with no option but to show the defender a straight red card.
Now playing with a man advantage, City affirmed control with a third just a couple of minutes later, with Tomas Galvez finding Dickson who produced a deft one-touch finish, rebounding off the post and creeping over the line to put the result truly beyond doubt.
In typical City fashion, we relentlessly kept up our pursuit of more goals and Bobb was unlucky not to add to the scoreline when his curling effort bounced off the post, before Mebude saw his shot well saved by United keeper Dermot Mee before the half-time whistle.
Into the second 45, United switched-up their tactics as they looked to limit the damage from the afternoon, often lining-up in a back five to shore up their defence.
City patiently kept possession as we looked to craft out an opening, but the United defence were able to hold firm for the time being.
The visitors did look for opportunities to break away on the counterattack, but a well-disciplined defensive showing shut out the Reds.
With 72 minutes on the clock, we managed to take our opportunity when Brandon Williams lost the ball to Terrell Agyemang who flashed the ball across goal towards Bobb who tapped home the fourth.
Breckin got himself in on the action, stroking home a composed left-foot shot from inside the area with four minutes left to play to make it 5-0.
And the scoring was rounded off when substitute striker Heskey stuck the ball into the roof of the net from close range to cap off a fine afternoon for the EDS.
HOW WE LINED UP
Cieran Slicker kept his place in City's goal, whilst captain Shea Charles moved into centre-back alongside Jadel Katongo. Tomas Galvez and Lakyle Samuel made up our full-back positions.
Alex Robertson and Kian Breckin were selected as a deeper- sitting midfield two, with Oscar Bobb playing in the more advanced number 10 role.
Dire Mebude took up his familiar position on the right with Micah Hamilton returning to the starting line-up on the left, both supporting central striker Will Dickson.
Manchester City Elite Development Squad
Starting XI: Slicker, Samuel (Agyemang 46'), Charles, Katongo, Galvez, Robertson, Mebude, Breckin, Dickson, Bobb, Hamilton (Heskey 64').
Substitutes: Murray-Jones, Borges.
Manchester United U21s
Starting XI: Mee, Jurado, Williams (Norkett 79'), Hardley, Aljofree, Iqbal, Forson (Wellens 46'), Gore, Mejia, Hansen-Aaroen (Wooster 27'), Emeran (Huddlestone 27').
WHAT IT MEANS
Barry-Murphy's side have returned back to the top of the Premier League 2.
We hold a one-point advantage over second place Chelsea, but have two games in hand over the London side.
The result also sees us keep up our remarkable goal-haul of 16 goals in the last three Premier League 2 games.
Our lads now head off on international break, with Robertson linking up with the senior Australia squad for the first time.
We'll return to domestic action with an away trip against Tottenham Hotspur on Monday 3 April, with kick-off at 19:00 BST.