The Lions were reduced to 10 men after the break when Jake Cooper committed a second bookable offence, but the third-tier outfit were quick to regroup and they held firm to punish the wasteful Foxes at the death.
The faltering Premier League champions come close to an opener in the 16th minute when Byron Webster was forced to produce a vital block at the near post to keep out Ahmed Musa, turning the ball behind for a corner.
Claudio Ranieri's side looked dangerous on the counter-attack, with Demarai Gray leading the charge, but Millwall weathered the early storm and applied pressure of their own before the half-time whistle.
Things looked bleak for Millwall when Cooper saw red for a reckless challenge on Musa in the 52nd minute, but Neil Harris's side continued to press forward undeterred.
They were almost caught on the break with 10 minute remaining when Okazaki collected substitute Marc Alrighton's cross in front of goal, but hesitation from the striker allowed Archer to position himself and make the block at point-blank range.
The miss proved costly for the Foxes as a through-pass from Lee Gregory sent Cummings in on goal as the clock reached 90, and the right-back showed strength and composure to shake off his marker and guide the ball beyond Zieler, firing The Den into a frenzy.
There were five anxious minutes of stoppage time to withstand, but Millwall's defensive mettle held up to see the League One minnows safely into the quarter-finals.