Vadaine Oliver and Levi Sutton put Bradford in a commanding position, before Will Alves and Tawanda Maswanhise restored parity on a wet and windy Tuesday evening at the University of Bradford Stadium.
A group stage point was secured after 90 minutes but the Foxes were able to double their tally for the evening by winning the subsequent shootout, with Kasey McAteer scoring the decisive spot-kick.
Making two changes from the side that drew away at Chelsea in Premier League 2 on Saturday, Lewis Brunt and Kian Pennant made way for Iestyn Hughes and Chris Popov.
It was likely to be a tough ask coming up against senior opposition just three days after a Premier League 2 fixture, but the visitors started brightly, without creating anything to show for their efforts.
The Bantams soon assumed control of proceedings, however, and applied pressure from a series of corners, the last of which led to a scramble in the Leicester box, but neither Bradford captain Yann Songo'o nor Kian Harratt, who saw an earlier effort deflect wide, could force it home.
Their opener did arrive on 11 minutes, though. A whipped cross from the left was met by Oliver, who powered a header past Chituru Odunze, establishing an early advantage for the hosts.
The forward looked in the mood for more and an audacious overhead kick, minutes later, wasn't far from troubling the Foxes' American shot-stopper either.
Odunze was called into action from a curling Harratt strike, keeping the ball out with his body, ahead of Jake Young's free-kick from the left being sent over the top of the crossbar.
Leicester's first shot on target came from Sammy Braybrooke's free-kick, as the skipper attempted to beat Harry Lewis, who was able to shuffle across to claim at at his near post.
A period of possession followed for the away side, as they grew into the game, with McAteer getting the better of Luke Hendrie, but again found Lewis in the way.
The increasingly influential Braybrooke then intercepted Timi Odusina's loose pass, playing through Popov, though the forward's lob failed to catch Lewis unawares.
Back at the other end, Luke Hendrie's cross to Oliver was saved acrobatically by Odunze to keep the score at 1-0 at the interval.
And he was needed again to stop Ryan East's effort low shot, but could not prevent Sutton extending the lead, when his shot deflected in four minutes after half-time.
Young fashioned an opportunity shortly after, skipping past two challenges before attempting to find the finish, but somehow missed the far corner.
That reprieve allowed Leicester to keep believing that they could make of a game of it. Braybrooke's hit from range soon kept Lewis on his toes, before Maswanhise met Joe Wormleighton's cross, striking the bar.
The deserved goal arrived via a neat finish from Alves, the midfielder finding the bottom corner with his left foot. The 17-year-old took aim again moments later, but this time it deflected into the arms of the 'keeper.
Leicester would not have to wait long for the leveller. A defence-splitting pass from Braybrooke found Maswanhise, and he made no mistake, converting first-time, during a whirlwind few minutes.
Both sides pushed for a winner in the closing stages. Young's latest set play crashed against the upright before Harratt was presented with a free header from East's free-kick, but diverted it over the bar.
Oliver and substitute Alex Gilliead were both denied by Odunze in quick succession, while Cover and Alves struck over from range for the away side, who entered stoppage time in the ascendency.
Terell Pennant, on as a substitute, had more time than he thought and dragged a shot well wide, before Harratt's overhead kick looked to have won it for the Yorkshire side, though Odunze somehow managed to save with his legs.
To penalties we went and after Odunze saved brilliantly from Sutton, Ethan Fitzhugh stepped up and scored, as did Paul Appiah after Gilliead squeezed his spot-kick underneath Leicester's stopper.
Emphatic penalties from both Dion Pereira and Braybrooke followed, but when Harratt sent his wide, McAteer took the opportunity to win the shootout, keeping calm to slot home and spark jubliant scenes from the Leicester Under-21s camp.
Major moment – A sensational comeback
Unable to find an equaliser when on top for a spell in the first 45, Leicester's youngsters were punished soon after the second half began. But they showed great character to come from two down and level, then holding their nerve in the penalty shootout to earn a hard-fought two points.
Who impressed? – Braybrooke creating
Strong performances all over the park were needed against League 2 opponents, but Sammy Braybrooke stood out in the centre of midfield, controlling the tempo for Leicester and claiming an assist for the equaliser.
Where do we stand? – Third in the group
City's youngsters sit third in Northern Group H, on two points, ahead of their final group game away to Sky Bet League 1 side Sheffield Wednesday on Tuesday 18 October (7pm kick-off). A win could see the Foxes progress into the knockout stages, if Burton Albion beat Bradford.
Coming up – Fulham (H)
Fulham Under-21s are the next visitors to LCFC Training Ground in Premier League 2 Division 1, on Monday 10 October (7pm kick-off).
The details...
City: Odunze; Wormleighton, Appiah, Wilson-Brown; Hughes (Cover 50'), Braybrooke (c), Cartwright (Fitzhugh 74'), McAteer; Alves, Maswanhise (T. Pennant 74'), Popov (K. Pennant 69').
Subs not used: Doherty, R. Nelson, Booth.
Goals: Alves 62', Maswanhise 66'.
All times BST.