After an even but goalless first half it was the hosts who gained an immediate advantage when Luke Chadwick fired home Jon Otsemobor's centre seven minutes after the restart.
Then the former Manchester United youngster doubled the Dons advantage when he was first to react after Jake Kean couldn't hold Daniel Powell's low effort.
Rovers' response was too little too late as David Goodwillie tapped home Fabio Nunes' centre on 83, and although Mauro Formica went close with a last minute header the ball agonisingly looped onto the roof of the net.
The home side deserved their victory and it they who can look forward to Saturday's third round draw.
With Rovers playing their fourth game in ten days it came as no surprise that Steve Kean made several changes for the cup clash against MK Dons.
There were seven changes in total from the win over Leicester City at the weekend as Jake Kean, Bradley Orr, Grant Hanley, Simon Vukcevic, Paulo Jorge, Ruben Rochina and Fabio Nunes all came into the starting eleven.
Of those coming in it saw a debut start for Paulo Jorge and Kean, Hanley, Vukcevic and Rochina starting for the first time this campaign.
Rovers' first visit to the stadium:MK started in lively fashion. Less than a minute was on the clock when Jake Kean was called into action, getting down to his right to push aside a shot from Daniel Powell.
Play was quickly switched to the opposite end and Rovers really should have taken the lead. Clever play by Edinho saw him feed Fabio Nunes and as Otsemobor delayed Nunes squad the ball back to Edinho but his shot was cleared on the line.
Both sides continued to create half chances with the home side having the better, Luke Chadwick firing over for the Dons, Ruben Rochina firing wide for Rovers.
Whilst Rovers approach play was neat and tidy it often lacked that final killer ball, the same couldn't be said for the opposition who again tested Jake Kean on 34 minutes, a nod down from Charlie MacDonald was met by Luke Chadwick to force Kean into a fingertip save.
On the stroke of half time Rovers fashioned another chance when Bradley Orr centred from the right but Edinho put his header over the bar.
In comparison to the first the second half was certainly slower to get going, but when it eventually sprang to life it was Karl Robinson's Dons who were much the better side and deservedly took the lead in the 52nd minute.
Grant Hanley saw his claims for a foul by Jon Otsemobor waved away as the full back got the better of Hanley on the byline and as he pulled the ball back for Luke Chadwick he swept the ball home at the second attempt.
Seven minutes later and Hanley was in the thick of it once more, this time defending superbly to keep out Powell's effort from the edge of the box.
David Goodwillie, Jason Lowe and Mauro Formica were all introduced but it was the hosts who grabbed a second on 67 minutes.
Neat approach play from MK Dons saw Daniel Powell let fly, Kean couldn't hold his effort and Chadwick reacted the quickest to poke home the rebound. There was a suspicion of offside but the goal was allowed to stand.
The home side looked comfortable but a David Goodwillie goal seven minutes from time gave the travelling side hope, the Scotsman nodding home Fabio Nunes' cross.
But it was MK Dons who could have grabbed a third goal two minutes from time, Rovers grateful for Paulo Jorge as he headed Shaun Williams' goalbound header off the line.
There was still time for a final Rovers chance but as Jason Lowe headed back Fabio Nunes' cross, Mauro Formica could only plant his header onto the roof of the net.
Whilst it was no secret that the cup would be behind the league in the order of importance, it will still be a huge disappointment to the manager that so many of the squad performed below par.
MK DONS: Martin, Otsemobor, MacKenzie, Williams, Gleeson (c), Potter, Bowditch (sub Ibehre 90 mins), MacDonald (sub Lowe 74 mins), Chicksen, Powell, Chadwick (sub O'Shea 77 mins).
Subs not used: McLoughlin, Alli, Galloway.
Goals: Goodwillie 83 mins.
ROVERS: Kean, Orr, Dann, Hanley, Markus Olsson, Vukcevic, Etuhu (sub Lowe 58 mins), Paulo Jorge, Fabio Nunes, Rochina (sub Formica 68 mins), Edinho (sub Goodwillie 58 mins).
Subs not used: Usai (GK), Martin Olsson, Morris, Ribeiro.
Goals: Chadwick 52, 67 mins.