Ben Reeves and Dean Bowditch struck in the first half of extra time to send Charlton packing from the FA Cup and ruining Karl Robinson's return to Stadium MK.
Daniel Powell poked Dons into a seventh minute lead before former MK full back Adam Chicksen restored parity midway through the first half.
With no goals in the second period, it took Reeves, a half-time substitute, just four minutes of extra time to restore Dons' lead, before turning provider for Bowditch three minutes later to book a third round spot and a trip to Brighton in January.
After winning his first game in charge at Stadium MK on Saturday, Robbie Neilson made four changes to the side which started, and beat AFC Wimbledon three days prior. Lee Nicholls replaced David Martin in goal, Ben Reeves and Samir Carruthers made way for Ryan Colclough and Daniel Powell, while Chuks Aneke made his first home start as he replaced Kieran Agard.
Neither side could find the back of the net in the opening tie back at The Valley, but it took Dons just seven minutes to open the scoring, thanks to Darren Potter. Although not the scorer, the midfielder did all the ard work in catching Joe Aribo unawares, tackling him 20 yards from goal to have play open out in front of him. Poking he ball into the box, Daniel Powell had the simplest of finishes to beat Dillon Phillips and give Dons the lead.
And the home side were good value for their lead, making all the headway in the match. Dean Bowditch was inches away from converting George Baldock's cross, while Powell had the ball in the net again but was flagged offside after a great move involving Bowditch and Aneke.
But while all eyes were on one former MK Dons staff member in the Charlton dugout, it was another, Adam Chicksen, who would come back to Stadium MK to haunt the home side. Chicksen, ghosting up the flank, picked up the ball 20 yards out, cut inside onto his right foot and, somewhat hopefully, chanced his luck with a low cutter. And it made it through a crowd of players, past Nicholls' out-stretched dive and into the net for the equaliser.
Back on level terms, the game too had far more of a balance. Charlton had found their feet, but with the Dons defence compact, it limited Brandon Hanlan and Lee Novak's chances. Novak in fact would leave the field before the half was up through injury, replaced by Morgan Fox.
Dons would have the best chance of taking the lead before the interval though, with Ryan Colclough carving a chance from seemingly nothing, but bending his shot just over the bar with Phillips looking beaten.
Dons boss Robbie Neilson replaced goal-scorer Powell with Ben Reeves at the break, but was forced to change his plans just 11 minutes into the second half when, after firing a shot just over, Baldock had to go off injured. It meant a big defensive reshuffle as Jack Hendry replaced him, and they were almost immediately pounced on by Ademola Lookman as he split the back line, but he couldn't beat Nicholls.
The game certainly had none of the gusto and panache of the game on Saturday, but it had flashes of quality. Reeves was desperately unlucky not to restore Dons' lead with 20 minutes to go as he nutmegged Aribo on half way before picking the ball up 30 yards out and fizzing in an effort arrowing towards the top corner, only to be denied by a brilliant Phillips save.
With extra time looming, Nicholls denied the visitors the chance of winning it in normal time as he got a foot to substitute Nicky Ajose's effort after the Charlton man sidestepped Paul Downing's challenge to pop a shot off just eight yards out.
But in seven minutes of extra time, Dons made sure of the result. Reeves fired Dons into the lead four minutes after the restart after good work from Kieran Agard on the right allowed him space to turn and pop a shot off from the edge of the box.
Three minutes later, it could have been all square when Nicholls midjudged a ball into the box which almost fell to Ajose to poke into the empty net. But from the restart, Reeves turned provider as he split the Charlton defence to allow Dean Bowditch to roll home his ninth goal of the season.
From there, seeing out extra time was fairly routine as both sides tired, Charlton offering nothing in retort.
Referee: Robert Jones
MK Dons: Nicholls, GB Williams, Lewington, Downing, Baldock, Upson, Potter, Powell (Reeves 46), Colclough, Aneke (Agard 61), Bowditch
Subs not used: Martin, Carruthers, Jackson, Tshimanga
Charlton Athletic: Phillips, Foley, Chicksen, Jackson (Johnson 80), Lookman, Botaka, Konsa, Hanlan (Ajose 72), Novak (Fox 40), Aribbo, Teixeira
Subs not used: Mitov, Ahearne-Grant, Charles-Cook, Umerah
Booked: Foley, Konsa, Potter