They looked comfortable for most of the contest and created plenty of chances, but a lack of clinical finishing and some sloppy defending meant they went home empty-handed.
Rhys Healey and Conor McGrandles both scored in the latter stages of the first half at Stadium MK, with Alex Gilbey adding a third after the break.
Ronan Curtis continued his fine goalscoring form by finding the net in stoppage-time, but it was just a consolation.
Kenny Jackett made one enforced change from the side that beat Wycombe on home soil on Boxing Day.
Ryan Williams picked up a groin injury in the early stages of that game and the man who replaced him, Marcus Harness, was handed a start.
That opened up a place on the bench, which was taken by teenage full-back Haji Mnoga, who signed his first professional contract at the start of the week.
Harness played a more advanced role than expected, playing alongside Ellis Harrison in what looked more like a 4-4-2 system.
Pompey took control of the contest right from the start and enjoyed plenty of possession and territorial advantage.
But for all the play they had in and around their opponents’ area, Lee Nicholls looked fairly comfortable between the sticks.
Ben Close and Curtis – the goal heroes against Wycombe – both had shots blocked in the early stages.
The hosts were looking nervy at the back and struggled to deal with some corners from Close, as well as Harness’ trickery.
Anton Walkes also looked a threat going forward down the left and sent a few dangerous deliveries into the box.
Nicholls was called into action on 15 minutes and did well to get behind a fierce long-range drive from the lively Harness.
The keeper conceded a free-kick inside the box after picking up Joe Walsh’s back-pass, but the wall did its job by rushing forward to block Curtis’ effort.
And the Dons then took the lead completely against the run of play, although the Blues were furious that referee Leigh Doughty failed to give a foul against James Bolton in the build-up.
Instead, Jordan Houghton launched the ball forward and Sean Raggett’s header was not hard enough to reach Craig MacGillivray, with Healey nipping in to score.
It got even worst for Pompey before the break, as Tom Naylor tackled Healey on the edge of the box and the ball ran kindly for McGrandles to impressively fire into the top corner.
MK Dons 2
Harrison did not emerge following the interval, with John Marquis coming on to replace him up front.
But it was the hosts who were first to threaten, courtesy of a long-range Gilbey attempt that MacGillivray tipped over the bar.
Pompey soon started to take control, though, and once again put plenty of pressure on their opponents.
But the ball just would not seem to fall kindly for them and although unconvincing, the Dons managed to get the ball clear.
And Nicholls was soon called into action to make two key saves in quick succession, first denying Marquis after the striker had been played through by Harness.
The resulting corner was flicked on by Naylor for Curtis at the far post, but the keeper was there to deny the Blues’ top scorer.
MK Dons still threatened at the other end, though, and Raggett had to head Dean Lewington’s free-kick just past his own post.
Then, from the resulting corner, a scramble in the box led to MacGillivray diving on the ball at the feet of Healey.
But Pompey were still pushing forward whenever possible and after some neat build-up play involving Curtis, Close and Harness, the latter’s shot was blocked.
Curtis then went close with a bending strike from outside of the box that Nicholls did brilliantly to turn behind.
Jackett made a double switch on 72 minutes, with Harness and Cannon racing from the pitch to be replaced by Gareth Evans and Brett Pitman.
Marquis was only able to hit a weak shot straight at Nicholls from a low Walkes cross, as time began to run out on the visitors.
A fracas near the touchline led to Walsh and Christian Burgess both being booked – and the Dons scoring a third to wrap the points up.
Pompey were awarded a free-kick, but it came to nothing and the hosts broke quickly up the field, with Gilbey lifting a neat finish over MacGillivray and into the net.
There was at least a reply from CURTIS, who turned home Bolton’s cross from close range right at the death, but there was not enough time for the Blues to launch another attack.
The loss was perhaps an unfair outcome for the visitors, who will hope to improve their away form when they visit Gillingham on New Year’s Day.
MK Dons (4-1-2-1-2): Nicholls; Brittain, Williams, Walsh, Lewington (c); Houghton; McGrandles, Kasumu; Gilbey (Reeves 90+1); Healey (Nombe 68), Mason (Agard 77)
Goals: Healey 35, McGrandles 42, Gilbey 84
Booked: McGrandles, Brittain, Kasumu, Walsh
Subs not used: Moore, Poole, Cargill, Boateng
Pompey (4-4-1-1): MacGillivray; Bolton, Burgess, Raggett, Walkes; Cannon (Pitman 72), Naylor (c), Close, Curtis; Harness (Evans 72); Harrison (Marquis 46)
Goals: Curtis 90+3
Booked: Harness, Burgess
Subs not used: Bass, Mnoga, Downing, Hawkins
Referee: Leigh Doughty
Attendance: 12,788 (5,083 Pompey fans)