Having beaten Premier League Sunderland in the previous round, Luton were well worth their 3-1 win over a much changed Charlton side thanks to goals from Steve Robinson, Matthew Spring and Drew Talbot.
The Addicks made ten changes from the side that beat Leicester on Saturday but still rocked Luton by taking the lead with only four minutes on the clock.
Dean Sinclair forced the ball home after the Hatters failed to deal with Izale McLeod's cross and Svetoslav Todorov's header.
And if Therry Racon's 25-yarder had dropped a couple of inches lower instead of smacking against the bar and McLeod's finishing twice with only Dean Brill to beat been less woeful, then the Addicks could have been looking at a comfortable half-time lead.
But Luton refused to panic and started to ask questions of their own.
Leading scorer Paul Furlong twice failed to connect with crosses and had a piledriver deflected wide, while Paul McVeigh and David Bell both missed good chances .
As Luton increased the pressure an equaliser seemed inevitable and it came from the unlikely boot of midfielder Robinson two minutes from half-time when he volleyed home a clearance to end an 18-month goal drought.
Luton continued to take the game to Charlton in the second half with Furlong, McVeigh and Spring going close, before Darren Randolph dived full length to save Dean Morgan's free-kick.
Both sides had chances to win as referee Andy D'Urso looked at his watch in preparation for full time, with Spring's volley flashing wide and Brill tipping over Darren Ambrose's looping header.
The first minute of extra-time almost provided Charlton with the breakthrough as Luke Varney forced Brill into a superb close-range save.
But the game swung decisively Luton's way at the end of the first period when Darren Currie's cross found the unmarked Spring, who headed his fourth goal of the season.
The icing on the cake came two minutes from time when Madjid Bougherra, indulging in keep-ball with Randolph, flipped over and Talbot ran through and gleefully slotted the third.