It went to penalties after both sides grafted for two hours in a largely inspiration-free zone, but when it came to the crunch Leicester had more bite from 12 yards, converting four of their spot-kicks to Leeds' two. The final piece of glory, however, fell to arguably their best player of the season, Muzzy Izzet, and the midfielder slotted his penalty calmly into the corner to seal a quarter-final against Fulham.
Despite having the majority of possession, Leeds never quite found the killer touch in front of goal, and fluffed their penalties badly, with Gary Kelly and Lee Bowyer missing the goal and hitting the crossbar respectively. Only Theo Zagorakis missed for the home side.
Leeds have been in action on four fronts this season, now down to three after this defeat, but although this was not the Premiership leaders' finest display of the season, they hung on even after being reduced to 10 men for the whole of extra time, when their captain Lucas Radebe was sent off for his second yellow card. Yet, even in the extra 30 minutes, it was the Yorkshiremen who showed true grit, coming close to ending the stalemate through the ever-impressive Harry Kewell.
David O'Leary's men will return to Premiership action this weekend, and that will be something of a novelty for his charges, as this match was their third consecutive Cup tie and fourth in five games. If their game at Chelsea on Sunday is level after 90 minutes, there is every chance they will be swapping ends while their opponents head for the showers.
But in a game desperately short on chances, Leeds can still feel slightly aggrieved they did not win from what little they did conjure up, for on the balance of play they shaded the tie. However, Leicester are not short on effort when the inspiration is missing, and they went closest of all with only two minutes of normal time remaining. From a Stefan Oakes free- kick, Matt Elliott, who also converted his penalty, saw his header cleared off the line by the valiant Matthew Jones. It was one of those games.
These two sides had met in the same stage of the competition last season and Leicester only won that tie with two goals in the dying minutes, but Leeds have come a long way in a short time, and their defence was unyielding to the very end.
However, if one of the early chances had been converted, it could have been a very different match. With 11 minutes gone, Kelly saw his 25-yard effort turned away by Tim Flowers and 14 minutes later Kewell glanced a header only inches wide.
Leicester did not even test Nigel Martyn in the first half and in the second there were slim pickings once more. The balance of the tie should have changed when Radebe was dismissed for bringing down Heskey, but Leeds hung on until penalties decided their fate.
Leicester City (3-5-2): Flowers; Taggart, Walsh, Elliott; Oakes, Izzet, Lennon (Zagorakis, 15) Savage, Impey; Cottee (Gunnlaugsson, f-t), Heskey. Substitutes not used: Arphexad (gk), Gilchrist, Campbell.
Leeds United (4-4-2): Martyn; Radebe, Woodgate, Harte, Kelly; Batty (Jones, 21) Bowyer, Bakke, McPhail; Kewell, Bridges (Duberry, f-t). Substitutes not used: Huckerby, Robinson (gk), Mills.
Referee: G Barber (Tring).