Competing at this stage of the competition for the first time since 1995, a much changed United side were outplayed by the League One Dons throughout.
A careless mistake from Jonny Evans allowed Will Grigg to open the scoring in the first-half from close range to send the Stadium:MK into delirium.
Former Brentford striker Grigg then added his and the Dons' second just after the hour mark, chesting the ball past a dumbfounded David de Gea.
Benik Afobe ruthlessly added a third after yet more poor defending from the visitors to put clear daylight between them and the 20-time top-flight champions.
Afobe's determination netted the hosts a fourth late on as the Dons completed a famous victory, and compounded the problems facing new United boss Louis van Gaal.
The 26,969 fans inside stadium:mk did their best to make United feel unwelcome as they took to the pitch, but in the early stages it appeared to have little effect as the Premier League club started well.
With 50 seconds on the clock, Danny Welbeck raced down the wing and found Hernandez at the back post, but the Mexican slipped just as he was about to pull the trigger.
Nick Powell then fired a 25-yard shot just over the bar.
Javier Hernandez punctured the Dons defence with a burst of pace, but he was pulled back for tugging Antony Kay's shirt.
Welbeck also broke through the back line in the ninth minute, but he could not test Martin.
De Gea had to race off his line to deny Grigg, who had given Reece James the slip to latch on to Darren Potter's headed through-ball.
Van Gaal was forced into a change when Shinji Kagawa was replaced by Adnan Januzaj following a clash of heads with a Dons defender.
Then came the moment Evans will not forget in a hurry.
The centre-half, under no pressure whatsoever, passed straight into the path of Ben Reeves inside the United box. The former Southampton player kept his cool and squared to Grigg, who slotted the ball past De Gea.
Evans held his head in his hands while the home fans taunted Van Gaal with chants of "You're getting sacked in the morning".
There was no immediate response from United. In fact, they were happy to go in at the break just one goal down.
Even the simplest of passes seemed beyond the 20-time English champions.
Hernandez, Anderson and Nick Powell were all guilty of wasteful play and Martin had nothing to do in the home goal.
Mamik Vermijl's clearance landed straight at the feet of Samir Carruthers, but he shot straight at De Gea.
Van Gaal replaced the poor Saidy Janko with another debutant, Andreas Pereira.
The League One side continued to hold their own after the restart and they thought they should have had a penalty when Dean Bowditch's shot struck Evans' arm. Stuart Attwell waved play on.
Welbeck offered a glimpse of the quality United needed with a fizzing shot that flew just wide.
Defensive vulnerabilities cost United again though as the Dons stunned the home crowd with a second goal.
Evans played a careless ball to Michael Keane, who had little time to clear. The hosts took advantage down the right through Reeves, who whipped in a flat cross which Grigg flicked past De Gea with his chest.
It was an audacious finish that would not have looked out of place at the Nou Camp, rather than the Moo Camp - the local name for stadium:mk due to the presence of the concrete cows nearby.
Seven minutes later a third flew in. Baldock gained some space down the left and found Reeves. He played the ball in behind to Afobe, who rifled past De Gea.
The home fans could not believe the scoreline. There was time for more excitement though. Afobe showed the fight United lacked, driving past three defenders before beating De Gea.
Martin pulled off a string of top saves to keep a clean sheet and put the icing on a miserable night for Van Gaal.