Nicky Forster finished off a flowing move to fire Reading ahead after 10 minutes as the home side dominated.
But Gareth Williams equalised for the Foxes, picking up David Connolly's pass and scoring at his second attempt.
Things got worse for Reading as Ricky Newman was cautioned twice and sent off before James Scowcroft headed home Leicester's 90th-minute winner.
The midfielder met Jordan Stewart's excellent cross from the left to seal the win over their Championship rivals.
Leicester boss Craig Levein:
"I thought we showed mental strength as well as playing some good football.
"It was a high tempo game and I thought Reading tired towards the end. They started very quickly and we made some bad decisions early on.
"I am not worried too much who we play in the next round. I am
trying to build a settled team with some momentum."
Reading: Hahnemann, Murty, Shorey, Sonko, Ingimarsson, Little, Harper, Newman, Hughes, Ferdinand (Owusu 69), Forster.
Subs Not Used: Young, Convey, Brooker, Morgan.
Sent Off: Newman (76).
Booked: Newman.
Goals: Forster 10.
Leicester: Walker, Maybury, Stewart, Dabizas, Heath, Gillespie (Dublin 89), Gudjonsson (Nalis 85), Williams, Tiatto, Scowcroft, Connolly (de Vries 79).
Subs Not Used: Hirschfeld, Makin.
Booked: Gudjonsson, Heath.
Goals: Williams 32, Scowcroft 90.
Att: 14,825
Ref: A D'Urso (Essex).