Garry Thompson fired the Shrimps into an early lead before efforts from Layton Ndukwu and Josh Knight put City on the cusp of securing all three points.
With seconds of the 90 minutes remaining, however, Elliott Osborne found the net to take the match to penalties, an ultimately disappointing outcome for Steve Beaglehole’s men.
While captain Hamza Choudhury and substitute Raul Uche Rubio were able to beat Danijel Nizic from 12 yards, Michael Rose, Sam Lavelle, Osborne and Adam Campbell converted for the hosts.
Despite this shoot-out defeat, City are awarded one point - which sees them climb to second in Northern Group A ahead of Wednesday's meeting between Fleetwood Town and Carlisle United.
Following an industrious start from both, it was the Shrimps who went ahead inside eight minutes when Vadaine Oliver dragged it across goal for Thompson to finish from four yards out.
The Foxes have already exhibited their resilience this term, however, and the scores were soon deservedly level through Ndukwu’s inventive low free-kick from 25 yards.
Morecambe emerged from the break in a bullish mood, with Oliver forcing Max Bramley into a last-ditch save before Steve Old rattled the woodwork from a tight angle.
Conditions worsened after the hour-mark with the wet surface resulting in a frenetic finale on the North West coast.
Kiernan Dewsbury-Hall very nearly laid a winner on for Eppiah with eight minutes to go, but the Belgian's header was collected comfortably by Nizic.
While unlucky on that occasion, Dewsbury-Hall’s delivery was the source of City’s second with 85 minutes on the clock - as Knight got a powerful header onto his corner kick.
However, joy soon turned to despair. As the fourth official signaled five minutes of added time, Osborne got up to nod the hosts level.
It was a dramatic turn of events which led to a chaotic final act. As Morecambe pushed for a late winner, they pilled everyone forward, including Nizic.
When he was caught deep in the Foxes half, Uche galloped forward and tried his luck from 40 yards, sending an ambitious low drive inches wide.
The real drama was yet to come, however, as the match went to penalties.
Rose opened the hosts’ account before Choudhury levelled, but Knight, taking his spot-kick immediately after as part of the ABBA system, was unable to put City ahead.
Lavelle then gave the hosts a crucial advantage before Osborne extended it. More disappointment followed for Beaglehole’s side when Josh Gordon was denied too.
It fell to Campbell to settle matters – which he did – but the visitors leave Lancashire knowing they still have a chance of reaching the knockout phase, sitting in second place.
Main moment
Morecambe's equaliser in the 90th minute was a cruel blow which turned the match on its head.
While City would have been forgiven for thinking they had done enough to secure all three points, it began a sequence of unfortunate events which saw them take just one.
Who impressed?
An ever-consistent performer, Hughes impressed again in Lancashire with a combative display alongside Knight, another impressive figure for City.
The summer signing from Chester has quickly made a name for himself in the Development Squad's ranks and he is a player Beaglehole relies on for stability at the back.
Where does it leave us?
On four points, Leicester are now second in Northern Group A. The top two sides from each pool qualify.
Their fate will ultimately be sealed on Wednesday when leaders Fleetwood (on six points) travel to third-place Carlisle United (three points).
Coming up…
The Foxes next entertain Portsmouth at Holmes Park in the Premier League Cup on Monday night (7pm kick-off), a clash you can watch live for FREE on LCFC TV.
Seven days later, Sunderland visit Whetstone in Premier League 2 (7pm kick-off).
The details...
Morecambe: Nizic, Old, Thompson (Turner 68), Fleming (Yawson 76), Oliver, Campbell, Conlan (Kenyon 83), Lavelle, Lund, Osborne, Rose.
Subs not used: Maher, McGowen, Jordon, Hawley.
Goals: Thompson 8, Osborne 90.
City: Bramley, Wood, Knight, Hughes, Johnson, Choudhury (c), Dewsbury-Hall, Kaba Sherif (Uche Rubio 73), Ndukwu (Shade 61), Gordon, Eppiah (Ughelumba 81).
Subs not used: Iversen, Heaven, Leshabela.
Goals: Ndukwu 25, Knight 85.
Referee: Robert Jones
Attendance: 432 (46)