Luca Barrington then added to our lead early in the second half before substitute Sammy Robinson also got in on the scoring act before Palmer set the seal on a superb display by completing his treble.
His stunning final goal set the seal on what was a fine night’s work for the City youngsters who further extended our lead at the top of the PL2 table
Back in action after the October international break, City were soon into our free-flowing, fluid best, teasing and testing the Leicester defence at every opportunity.
The attacking midfielder ghosted onto Oscar Bobb’s deft through ball before swivelling inside and firing a crisp left shot just over.
However, Palmer wasn’t to be denied for long.
Within two minutes he was picked out by Romeo Lavia’s smart assist and drilled a low shot home to give Barry-Murphy’s youngsters the early advantage.
It was a further demonstration – if any were needed – of Palmer's voracious appetite and desire for the game
City then saw strong appeals for a penalty turned down after Luca Barrington’s goal bound shot appeared to strike a Leicester arm.
Referee Elliott Swallow was unmoved, however.
Having been in complete control City then had a huge let off on 41 minutes. Having come out of his box to clear a long ball, keeper Miki van Sas then misplaced a pass instead finding Leicester’s Jake Wakeling 20 yards out.
However, with van Sas stranded outside his box, the Foxes striker’s shot was fortunately too strong and cleared the bar.
The visitors were almost immediately made to pay for that miss as Palmer doubled his and City’s advantage on the stroke of half time.
With Leicester failing to clear their lines, Palmer seized the ball on the edge of the box and fired home a low shot to send City in 2-0 up at the break.
A mountainous task got even steeper for the visitors three minutes after the restart with Luca Barrington marking his EDS debut in superb style.
The youngster cut in from the left before firing a low shot home to further extend our advantage.
City's dominance was further reinforced on 78 minutes when substitute Sammy Robinson found the target, the full-back scoring from close-range after a rebound off Leicester keeper Brad Young.
But the final word deservedly went to Palmer who sealed his hat-trick with a brilliant curling shot to round off a terrific performance.
How we lined up
What it means
With second-placed Arsenal having lost 3-0 at Liverpool earlier in the day, the victory extended City’s lead at the top of PL2.
We now sit four points clear with 20 points from eight games and are now the only unbeaten team in PL2.
Brian Barry-Murphy’s side are back in action on Tuesday when we resume our UEFA Youth League campaign away to Club Brugge Under-19s.
Kick-off in Belgium for our third group fixture is slated for 12.30pm (BST).
News about Man City v Leicester
City action man Palmer insists: 'I am doing what I love!'
Cole Palmer reflected on an extraordinary Saturday that saw him come on as a substitute for City’s first team in our 2-0 win over Burnley – then barely two hours later score a hat-trick for our EDS side - by insisting: “I am doing what I love.” Read more.
Match highlights: City EDS 5-0 Leicester
Action man Cole Palmer fired a stunning hat-trick to help inspire City’s Elite Development Squad to an impressive PL2 victory over Leicester at the Academy Stadium. Watch more.
Watch City EDS v Leicester on CITY+
City’s Premier League 2 clash with Leicester Under-23s will be broadcast live on CITY+. Watch more.