The visitors carried a one-goal advantage into the break thanks to George O’Neill’s finish, but the young Foxes drew level just three minutes into the second half through Harvey Barnes, before Darnell Johnson wheeled away in celebration in the closing stages after heading in at the back post.
City were fully aware of their potential achievements going into the clash, knowing that the last side to reach the semi-finals completed that feat 28 years ago.
It was a confident start from the hosts as the game’s opening chance fell to Keenan King, who had already scored two goals in this season's competition going into the tie. The striker mustered up the first opportunity of the night, forcing Birmingham shot-stopper Jake Weaver into a low save with five minutes gone.
With City controlling possession in the early stages, Brandon Fox was next to test the opposition ‘keeper. The winger’s near-post effort nearly caught Weaver off guard, but the visitors’ No.1 recovered well and tipped wide.
Layton Ndukwu, who netted City’s second goal in the 2-0 win at Southampton in the previous round, then curled an effort from 25 yards which forced Weaver into another save before Elliott Moore’s header from the resulting corner was scrambled away.
A fine challenge from Cedric Kipre prevented O’Neill from bursting through City’s defences, while Sam Deadfield’s low drive hammered Max Smith-Varnham’s side-netting as Birmingham started to settle following the hosts’ early dominance.
An instinctive save from Smith-Varnham kept the game goalless on the half-hour mark, as the City goalkeeper denied David Popa with his legs, before O’Neill blasted the rebound over from a difficult angle.
Birmingham upped their offensive pressure and it paid off on 36 minutes. O’Neill was first to a flick-on after a throw-in from the right, and the lively No.11 drilled in from 10 yards to give his side the lead.
The visitors came close to doubling their advantage just minutes later. Kyle McFarlane raced down the left flank before pulling back for O’Neill, who was only denied his second of the game by City captain Ben Chilwell’s goal-saving block – 1-0 to Birmingham at half-time.
City responded brilliantly after the break. Barnes, who netted two minutes into the second half in the triumph over Brighton on Saturday, latched onto a through-ball and calmly slotted in past Weaver to level the game up at 1-1 on 48 minutes.
Chilwell connected with Fox’s corner just after the hour mark, but couldn’t generate the desired power to beat Weaver as the left-back nodded wide.
Kipre’s glancing header from a Matty Miles corner flew just wide of the Birmingham upright, while at the other end, Darnell Johnson did well to quash McFarlane’s threat from the left wing with a timely interception.
Barnes tried his luck from range on 68 minutes, firing over with his left foot from 25 yards, ambitiously searching for the top corner of Weaver’s net.
A ferocious long-range strike from Fox looked to have bounced in off the crossbar with 80 minutes on the clock, but instead dropped onto the line before Birmingham cleared the loose ball.
The Blues were next to hit the woodwork with six minutes to play as Charlie Cooper’s corner crashed off Smith-Varnham’s upright, while Moore was on hand to block a goal-bound follow-up.
But it was City who would strike the decisive blow with just two minutes to play. Miles’ floated free-kick found defender Johnson, who headed in past the defiant Weaver to complete the comeback.
The result will see Leicester play either Manchester City or Crewe Alexandra – who are set to play their sixth round tie on Monday evening – over two legs for a spot in the final of the competition.
CITY: Smith-Varnham, Johnson, Chilwell (c), Choudhury, Moore, Kipre, Ndukwu, Miles, King, Barnes, Fox
SUBS NOT USED: Knight, Bramley, Fura, Bailey, Muskwe
GOALS: Barnes 48, Johnson 88
BIRMINGHAM: Weaver, Cotton, Bernard (c), Cooper, Harding, Martin, Dunbar, Deadfield (Bailey 89), McFarlane, Popa (O’Keeffe 73), O’Neill
SUBS NOT USED: Smith, Seddon, Lubala
GOAL: O’Neill 36
ATTENDANCE: 1,696
REFEREE: Stephen Martin