The Foxes, who went into the game having won 13 in 15 matches, knew a victory at EBB Stadium would have taken them above the Blues on goal difference at the summit.
City's starting XI included four changes from the 2-1 victory over Dinamo Zagreb on Monday, as Viktor Johansson, Calvin Ughelumba, Bartosz Kapustka and Josh Eppiah returned.
The first chance for the visitors came after eight minutes as Luke Thomas lofted a high ball in for Ali Reghba, who nodded it over the crossbar from a tight angle for Leicester.
Midway through the first half, meanwhile, Blues goalkeeper Karlo Žiger was called upon to make an excellent fingertip save to deny Reghba again after the Irishman ran through at goal.
Chelsea went ahead, though, on 28 minutes and it was a remarkable individual strike from Tino Anjorin, who galloped into the box and arrowed an effort into the far bottom corner.
Before the break, the home side needed another impressive save from Žiger to deny the Foxes an equaliser as Ughelumba's half-volley was tipped over the bar by the young Croatian 'keeper.
Luke McCormick forced Viktor Johansson into a decent stop just after hour-mark but it was 2-0 to the Blues, though, as Henry Lawrence pounced to convert the rebound for his side.
Tyrese Shade was introduced shortly afterwards in Aldershot and just 10 minutes later he'd halved the deficit for City, twisting and turning inside his man before sending a stylish finish past Žiger.
Leicester kept pushing for an equaliser, which would keep them within touching distance of the leaders, and Thomas' header, from an Ughelumba cross, was directed straight at the home shot-stopper.
It came in the second minute of added time as Callum Wright's corner landed straight onto the head of Darnell Johnson to thump a header past Žiger, sparking jubilation from the visitors.
Major moment
The time was ebbing away for Leicester's youngsters, who may have started to contemplate a defeat by Chelsea which would have left them six points adrift of the leaders.
Up stepped Callum Wright, the scorer of a brace on Monday, to send in a perfect cross, met by the onrushing Darnell Johnson, who confidently met it, sending it crashing into the back of the net.
Who impressed?
Speaking on LCFC TV's live match coverage, former Foxes forward James Scowcroft said: "There were several very good displays, but I quite like the look of Luke Thomas - his delivery into the box was superb and he really stood out for me."
Where does it leave us?
City's Under-23s climb to second in Premier League 2 Division 1, above Derby County by a margin of two points, although the Rams have a game in hand.
On 29 points, Leicester remain three behind leaders Chelsea, who are yet to suffer a defeat in the league so far into the 2019/20 campaign.
Coming up...
The Foxes travel to Rodney Parade to face Newport County in their rearranged Leasing.com Trophy Quarter-Final tie on Tuesday (7pm GMT kick-off).
Whoever wins out in South Wales, meanwhile, will host Salford City in the last-four stage of the competition.
The details...
City: Johansson; Johnson (c), Hughes, Ughelumba; Daley-Campbell (Shade 63'), Kapustka (Pennant 83'), Leshabela, Thomas, Wright, Eppiah, Reghba
Subs not used: Stolarczyk, O'Connor, Hulme
Goals: Shade 74', Johnson 90+2'
Images: Clive Howes