The League One side had to play the majority of the second half without Jake Cooper after he was sent off in the 51st minute for a second bookable offence.
But the deficit only inspired Millwall to a famous victory with Cummings finding the net in the 90th minute to heap more pressure on Claudio Ranieri and his beleaguered team.
With more than one eye on their Champions League trip first-leg clash at Sevilla next week and their Premier League encounter against Liverpool a week on Monday, Ranieri made 10 changes to his side which lost at Swansea.
Jamie Vardy and Riyad Mahrez were relegated to the bench while Demarai Gray was the only survivor from the 2-0 defeat at the Liberty Stadium - a result which leaves Leicester hovering dangerously above the relegation zone.
Millwall, sixth in League One, may have sensed an opportunity to shock the Premier League champions, but it was Leicester - despite the changes to personnel - who enjoyed the better start.
And it was Gray who provided the first real opportunity of the match
Bartosz Kapustka floated the ball into his path, and the youngster cut back in on his right foot only for his curled effort to fall wide of Jordan Archer's post.
As Vardy, who has failed to score since last year, warmed up on the touchline, Shinji Okazaki found himself through on goal
Off-balance however, Archer managed to parry his shot away.
Ahmed Musa was there for the follow-up, but his quick-fire shot was superbly blocked by Byron Webster
Okazaki then saw his header from the resulting corner magnificently palmed away by the Millwall stopper.
The Foxes, despite their miserable recent form, were upping the ante and it only seemed a matter of time before they would open their account
But despite an impressive opening 30 minutes, Leicester failed to find the back of the net and on this bobbly pitch, roared on by a raucous crowd, the hosts ended the first half on top.
Calum Butcher's header from a corner called Ron-Robert Zieler into action for the first time and a goal-mouth scramble ensued moments before the interval
Cooper was booked for his over-zealous attempts to snatch the ball out of Zieler's grasp
Nevertheless, these were encouraging signs for the south London outfit.
But just six minutes after the interval Millwall were reduced to 10 men when Cooper was sent off for a rash challenge on Musa.
It should have provided the spark for Leicester to go on and win the tie, but it appeared to have the opposite effect with the hosts continuing to cause the English champions problems
With 18 minutes to go, and his side now on the back foot, Ranieri called for Vardy
Moments later, the England international had Archer scrambling to his far post as his 20-yard shot fizzed wide.
Then with 10 minutes to go, Okazaki had the perfect chance to win the tie
Marc Albrighton's cross fell into his path inside the six-yard box, but the Japanese forward failed to convert it past Archer.
The tie appeared to be heading for a replay before substitute Lee Gregory chested the ball into the path of Cummings who made no mistake as he coolly slotted the ball past Zieler
Millwall survived five minutes of injury time before ecstatic home supporters ran on to the pitch to celebrate the win
Source : PA