City's youngsters headed into the last-eight tie after overcoming holders Aston Villa, Crewe Alexandra and AFC Bournemouth in earlier rounds, while United were buoyed by their rich heritage in the competition after lifting the iconic youth trophy 10 times – more than any other side.
Coach Adam Barradell made four changes to Leicester's XI following the 4-1 success over Tottenham Hotspur in the U18 Premier League South, with Ben Nelson, Sammy Braybrooke, Joe Wormleighton and Will Alves coming in for Ben Grist, Jesper Kutshienza, Brandon Cover and Jack Butterfill.
It was the young Foxes who started on the front foot at the Theatre of Dreams, with United goalkeeper Radek Vitek swiping at Braybrooke's deep free-kick into the area. The second of two Braybrooke corners inside the opening five minutes, on the other hand, was nodded into Vitek's gloves by Nelson.
With 12 minutes on the clock, in front of a sizeable home crowd in Manchester, American forward Zach Booth ran at goal, twisting and turning past his man, before seeing a low drive deflect behind for a corner. Braybrooke's ball in then came to Booth again in the area, but his header was off target.
Nelson then had to be alert to stop Charlie McNeill from working an opening on the counter after Wormleighton's cross was cut out by Vitek at the other end. For the opening 20 minutes, it was Leicester's Under-18s who were dictating the play, keeping possession effectively and venturing forwards with ambition.
United, though, were starting to present a threat. Midway through the first half, Alejandro Garnacho took it upon himself to charge into the box, necessitating Foxes skipper Harvey Godsmark-Ford to race back and hook his his cross away. McNeill was there, waiting to convert, if not for that timely interception.
Another United breakaway was then cut short by Jahmari Lindsay's late challenge on McNeill just inside the City half, earning the tie's first yellow card. Lindsay was involved again, at the opposite end, robbing Sam Mather and teeing up Booth. The 17-year-old, though, blazed over from the edge of the area.
Leicester were deservedly ahead on the half-hour mark. Their high press was rewarded when Wormleighton nipped in to take the ball away from Sam Murray on the right channel, curling a low cross into Chris Popov – playing against his former club – who took a touch and saw his effort squirm past Vitek.
Mather was narrowly off target from range for the home side moments later, but the young Foxes quickly looked to assert their dominance. Vitek was being kept busy and the Czech 'keeper was there again to stop Alves' low drive from finding the net in the bottom left corner.
City were on top but warnings of United's quality were there as Garnacho's curler required a solid stop from Arlo Doherty on 40 minutes. The half ended in frustration for Leicester when Garnacho restored parity on the scoresheet seconds later, arrowing a free-kick into the bottom corner from 25 yards out.
Mather then broke free down the middle at the outset of added time, looking to send the visitors in at the break behind, but Doherty was on hand to save well. After the break, the complexion of the tie changed, but it began with Alves cutting inside his man and stinging the gloves of Vitek from range.
It was becoming an end-to-end cup tie. Eight minutes into the second period, a flowing Man Utd move involved McNeil belting the ball at goal from inside the area, sparking Doherty into a fine outstretched save. Alves then surged forwards, with Vitek saving his drive and Popov's attempt to convert the rebound.
Just after the hour, Lindsay flashed a delivery across the face of goal, with Popov bursting his lungs to get on the end of it, but Leicester's No.9 couldn't get there. McNeil then powered the ball into Doherty's side-netting, before Jack Butterfill replaced Booth for the young Foxes.
A golden opportunity landed to McNeil with 20 minutes to play after the United striker took the ball from Thomas Wilson-Brown. Doherty, however, rushed from his line to smother it and allow Wilson-Brown to hack the ball away. Unlike the first half, it was the Red Devils in the ascendancy now.
Cover was introduced for the final 15 minutes, taking the place of Henry Cartwright, as the Club's Under-18s looked to hold onto possession for longer spells. McNeil and Garnacho were proving to be a menace for Leicester, though, and the latter hit a wild effort high and wide for the Red Devils.
Nelson was also withdrawn, due to injury, with Ben Grist taking to the pitch late on. A finely poised tie seemed destined for added time as McNeil skidded another strike wide of Doherty's Leicester goal. However, Garnacho's 89th-minute goal, drilled into the far corner, was a crushing blow for City's youngsters.
One last chance came their way at the end of five added minutes, but Godsmark-Ford couldn't direct Braybrooke's free-kick towards goal. The Club's youngsters, though, can take pride from their run in the competition and find reasons for optimism in other formats for the remainder of 2021/22.
Major moment
After defending so valiantly as Man Utd unleashed waves of forays into the final third late on, it was a frustrating end for the young Foxes, who conceded to Alejandro Garnacho's admirable hit on 89 minutes.
Who impressed?
It was very much a game of two halves for Leicester, who shone in the first 45 minutes, but were forced to defend for long spells after the break. Will Alves, however, was a threat for the visitors throughout, exhibiting a wide array of skills, while Chris Popov was alert to score the opener too.
Where do we stand?
City's Under-18s exit the FA Youth Cup at the quarter-finals stage, but they remain in the semi-finals of the Premier League Cup and sit third in the U18 Premier League South table.
Coming up…
A trip to Birmingham City is next up for the young Foxes in U18 Premier League South on Tuesday (1pm kick-off), before heading to Crystal Palace next Saturday (12pm kick-off). A fourth successive away game, also in the league, takes place at Aston Villa on Tuesday 8 March (11am kick-off).
The details
City: Doherty; Nelson (Grist 81'), Godsmark-Ford (c), Wilson-Brown; Wormleighton, Cartwright (Cover 75'), Braybrooke, Lindsay; Booth (Butterfill 66'), Popov, Alves.
Subs not used: Chibueze, Kutshienza, Lewis, Briggs.
Goals: Popov 29'.
All times GMT.