Paul Groves’ men went into the break a goal up after a near faultless first-half display thanks to Lewis Grabban’s first goal for the club.
MK Dons were reduced to ten men shortly afterwards as midfielder Alan Smith was sent off for a dangerous tackle on Harry Arter.
Last season’s play-off semi-finalists improved in the second half, and Daniel Powell lifted the ball over Shwan Jalal just after the hour mark to earn the visitors a point.
The Cherries piled on the pressure in the dying stages, and had a goal disallowed 15 minutes from time, but couldn’t find their way past a stubborn Dons defence.
Groves made three changes to the team that started Saturday’s League One opener at Portsmouth. Steve Cook made his first appearance of the season, while Arter and Grabban were recalled, with the summer
signing preferred to Wes Thomas up front.
The visitors enjoyed most of the early possession, but both Dean Bowditch and Dean Lewington failed to test Jalal with long range strikes.
The Cherries began to find their rhythm and took the lead after 15 minutes through Grabban.
He collected Charlie Daniels’ mishit shot just inside the penalty area before calmly slotting the ball past David Martin for his first goal in Bournemouth colours.
Just a few minutes later Smith was shown a straight red card for a reckless two-footed tackle on Arter.
Arter was lucky to emerge from the challenge unscathed and was able to continue after treatment from physio Steve Hard. It was the third red card in as many games for Karl Robinson’s side.
It appeared that Smith’s dismissal would prove to be a pivotal moment in the game, and despite Robinson sending on Luke Chadwick to bolster his midfield, the Cherries were firmly in control.
With the Dons struggling to make their way out of their own half, Simon Francis, Cook, Daniels and Arter all went close to extending the lead.
Joe Partington, who impressed throughout with a composed display at the heart of midfield, forced a save from Martin with a powerful drive after playing a neat one-two with Francis.
Steve Fletcher was introduced at half-time in place of Arter for his first competitive appearance since turning 40 in July.
MK Dons had emerged from the changing rooms with more resilience, and Bowditch missed a great opportunity to the level the scores when he sidefooted wide from ten yards out.
After Partington had curled his shot just wide, MK Dons had a penalty appeal turned down.
Powell had gone one on one with Jalal but captain Miles Addison dispossessed the pacy striker with a timely intervention.
Barnard thought he scored the second goal of his loan spell at the Goldsands Stadium when he prodded Fletcher’s knock down into the net, but his celebrations were cut short as the assistant referee called the on loan striker offside.
MK Dons were pushing for an equaliser and Powell provided just that as he dinked the ball over Jalal with 30 minutes to play.
The Cherries were later denied by the woodwork as Cook headed Eunan O’Kane’s corner against the bar.
Fletcher had become the focal point for the Cherries attacks and Marc Pugh should have hit the target after he had been teed up by the veteran forward.
As Barnard’s header rolled wide and the Dons seemed content with a point, Groves sent on Matt Tubbs with his second change of the evening.
As time ticked away Pugh came close to forcing a winner as his shot bounced agonisingly wide via a deflection off substitute Luke Chadwick.
It wasn't to be and the Cherries will now turn the attentions to Preston, who visit the south coast on Saturday.
Cherries: Jalal, Francis, Cook, Addison, Daniels, O’Kane, Partington, Arter (Fletcher, h/t), Pugh, Grabban (Tubbs, 78), Barnard.
Unused substitutes: Flahavan, Zubar, Gregory, Wakefield, Thomas.
Goal: Grabban (17).
MK Dons: Martin, Ostemobor, Lewington, MacKenzie, Potter, Bowditch (O’Shea, 90), MacDonald (Chadwick 21), Smith, Chicksen, Powell, Lowe (Ibhere, 70).
Unused substitutes: McLoughlin, Ali, Galloway.
Goal: Powell (61)
Sent off: Smith.
Attendance: 5, 407 (271 MK Dons fans)