Striker turned midfielder Aaron Wilbraham did the damage with two goals, his second coming in the last minute.
The visitors could well have won by a far greater margin had striker Scott Taylor been more clinical, as the former Blackpool man had enough chances to have claimed the match ball.
Barnsley boss Andy Ritchie, mindful of the fact that his side have an important Championship game at Preston on Friday, retained only Antony Kay and Dale Tonge of the players who had begun the win against Wolves last weekend.
In contrast, the Dons had a seasoned look about them and their play in the first half deserved perhaps more than the one goal they scored.
They made the breakthrough in the 28th minute when full-back Dean Lewington delivered a deep cross from the left and Wilbraham rose high at the far post to send a firm header beyond Barnsley's 18-year-old goalkeeper Vito Mannone, on loan from Arsenal.
Teenage striker Michael Coulson was Barnsley's liveliest threat and his express pace took him away from Lewington and into the box, but his pull back was cleared by Dons defender Ben Chorley.
A silly mistake by home skipper Kay then let in Taylor but his rising drive was magnificently tipped over by Mannone, before the resulting corner saw Chorley's downward header cleared off the line by Anthony McParland.
Barnsley had the edge in the early stages of the second half and Tommy Wright, who wasted a glorious chance in the opening 45 minutes, had a looping header cleared off the line by the well-placed Lewington.
Ritchie sent on Michael McIndoe just after the hour mark and he brought Barnsley level in the 66th minute with a lovely low left-foot shot.
However, the Dons always threatened going forward and, after Taylor had squandered two more glorious chances, Wilbraham popped up with a deflected winner in the dying seconds.