Luton started the game well but first-half goals from Demarai Gray and former Hatter James Justin put the Premier League side in control at the break.
Youri Tielemans and Kelechi Iheanacho got themselves on the scoresheet towards the end of the game to ensure the Foxes were in the hat for the fourth round of a competition they have ambitions of winning.
Town were not fearful of the tricky task ahead of them initially, even when Marc Albrighton’s long-distance strike was well saved and Christian Fuchs arrowed a left-footed piledriver over the bar.
The Hatters were well in the game throughout the first half-an-hour, playing mainly through Callum McManaman, who was a threat for the Foxes to try and contain.
But the Premier League side took the lead in the 34th minute after a sustained period of pressure, as Gray swept home as Ayoze Perez dummied Albrighton’s low right-wing corner.
Leicester fans were celebrating again four minutes later but their joy was short lived, as Perez was ruled to be offside after he latched onto Tielemans’ through pass and chipped the ball over James Shea.
But their second did come a minute before half-time, and it was courtesy of Justin on his return to Kenilworth Road.
Tielemans played a perfectly weighed ball over the top and the local lad arrived at the back post to emphatically finish beyond Shea.
Leicester were pushing for a third goal straight after the break and Shea was called into action a number of times to keep the Hatters in the game.
But the Town had a fantastic chance of their own in the 68th minute. Luke Bolton surged forward from right-back and found Izzy Brown on the edge of the box, but his low drive was saved by Danny Ward and McManaman's shot on the rebound was deflected behind.
That was a chance the Hatters would rue as the Foxes made them pay when Tielemans further extended their lead in the 79th minute.
The ball fell loose to the Belgium international from 12 yards out and despite not hitting his effort cleanly, it bounced high off the turf and into the top corner.
Leicester weren’t done though as they scored a fourth in the 86th minute. Substitute Kelechi Iheanacho capitalised on a loose ball in the Town defence and chipped his effort over Shea, who got fingertips to it, he couldn’t keep it out.
The Town had a goal ruled out for offside in the dying embers after Sheehan’s corner was flicked on by Harry Cornick to Kazenga LuaLua, who poked the ball into the net, only for the cheers to be cut short by a linesman's flag.
Luton will not be too disheartened with a loss and subsequent exit from the Carabao Cup, given how good the opposition, who currently occupy third spot in English football, were.
The Hatters switch their attention towards a tough away trip to Blackburn on Saturday, before returning to Kenilworth Road for the visit of Millwall next Wednesday.
TOWN: Shea, Bolton, Jones, Sheehan (C), Potts, McManaman (LuaLua 72), Butterfield, Berry, Mpanzu, Moncur (Brown 60), Lee (Cornick 60). Subs not used: Tunnicliffe, Pearson, Sluga (GK), Bree
LEICESTER: Ward, Justin, Morgan (C), Evans, Fuchs, Albrighton, Tielemans, Ndidi (Choudhury 77), Praet, Gray, Perez (Iheanacho 70). Subs not used: Schmeichel, Vardy, Barnes, Amartey, Pereira.
Goals: Gray 34, Justin 44, Tielemans 79, Iheanacho 86
Referee: Matthew Donohue
Attendance: 8,216 (1,500 away fans)
