James Tilley sent the visitors into a shock lead from the penalty spot in the 19th minute, but Noni Madueke levelled with a spot kick of his own in first-half stoppage time, before Enzo Fernandez came up with the winner in the 72nd minute of the contest in the English capital.
As expected, Blues boss Mauricio Pochettino rung the changes for the cup contest, and there was interestingly a start and ultimately a full 90 minutes for Marc Cucurella, who is currently being heavily linked with a loan switch to Manchester United.
AFC Wimbledon were awarded a penalty in the 18th minute of the contest when Chelsea goalkeeper Robert Sanchez was penalised for a foul on Harry Pell, and Tilley stepped up before finding the back of the net with a powerful strike.
Chelsea came close to a leveller in the 25th minute, with Ian Maatsen's effort deflecting just wide of the post, and it was not a surprise that the Premier League outfit were the side dominating the ball.
However, Joe Lewis was impressing in the middle of the AFC Wimbledon defence, with the League Two outfit managing to resist the pressure from a much-changed Chelsea outfit.
Madueke bent one just wide of the away side's goal in the 39th minute, but Chelsea managed to level the scores from the penalty spot late in the first period, with Madueke finding the back of the net after the attacker had been brought down inside the box by AFC Wimbledon's Alex Pearce.
Alex Bass made a smart save in the 49th minute to keep out a strike from Nicolas Jackson, before Pell passed up a decent chance down the other end two minutes later, firing wide from inside the box.
Bass was again called into action in the 56th minute to deny Conor Gallagher, before the AFC Wimbledon goalkeeper made an even better save to deny Fernandez 20 minutes from time.
The pressure eventually paid off in the 72nd minute, though, with Fernandez firing into an empty net from distance following a mistake from Bass, who had come out to confront Maatsen, but he smashed the ball into the Chelsea defender and it fell for Fernandez.
Jackson, Maatsen, Fernandez and Gallagher all had chances to add to the scoring late on, but Chelsea ultimately declared at two, which proved enough to advance into the next round of the competition.
Chelsea will continue their Premier League campaign at home to Nottingham Forest on Saturday, while Wimbledon will travel to Newport County in League Two on the same afternoon.