Jordi Gomez scored a fine free-kick late on to deny the Dons a point at Ewood Park.
Alex Revell looked to have secured a point in the final five minutes but Gomez struck his second of the afternoon in injury-time.
The Dons had initially led through Samir Carruthers but goals from Gomez and Elliott Bennett put Rovers in front before a frantic finale.
Carruthers, back after suspension, and Nicky Maynard replaced Josh Murphy and Alex Revell in the starting XI for the clash in Lancashire. David Martin, Matt Upson, Carl Baker and Ben Reeves remain sidelined through injury.
The Dons settled well and enjoyed some good early possession, however, it was the hosts who had the first chance of the afternoon on 13 minutes when Chris Brown fired his low effort across the face of goal.
As the 20-minute mark approached, Carruthers almost found Nicky Maynard with a through-ball before Jake Forster-Caskley couldn’t pick out a team-mate following some nice build-up play.
The men from MK1 were playing some good football, typified by Forster-Caskey’s dummy which led to a foul on Carruthers 25 minutes in. After his goal at Derby County, no-one was taking the ball of Forster-Caskey, who forced Jason Steele to push his free-kick against the crossbar.
Darren Potter then drilled down the throat of the Rovers keeper as the Dons really began to control proceedings, with the home side unable to get on the ball or trouble Karl Robinson’s men.
On a rare foray forward for Rovers, Brown mis-timed his header from an Elliott Bennett cross but, in truth, that was the first time Paul Lambert’s had threatened.
The Dons’ pressure finally told on 36 minutes when Bowditch latched on to Forster-Caskey’s clever pass and fed the returning Carruthers, who cut inside before firing an unstoppable effort under Steele from 20 yards.
Rovers almost levelled immediately but Brown sent his rebound over the bar after Jordi Gomez had been brilliantly denied by Cody Cropper from the edge of the area.
George Baldock was in the right place at the right time to clear at the start of the second half while, at the other end, the Dons broke and Bowditch fired off target from the edge of the box.
Rovers were level on 53 minutes when Gomez headed home after Cropper and Baldock had initially cleared efforts off the line from a corner.
The hosts then enjoyed a good spell of pressure including a header over the top by Shane Duffy from an out-swinging corner.
Murphy was introduced just after the hour mark and he was on the ball immediately, driving at the Rovers defence and forcing Grant Hanley into an important clearance.
But it was the hosts who hit the front on 71 minutes when the Dons failed to clear and Bennett drove home from 20 yards.
The men from MK1 came close to levelling matters five minutes later but Bowditch wasn’t able to direct his sliding effort at the back post on target.
Cropper ensured the Dons remained at 2-1 with a fine stop to deny Danny Graham from 12 yards with just over 10 minutes remaining.
Murphy was looking lively down the left and he won a corner on 84 minutes, which Joe Walsh flicked on towards Dean Lewington but he fired over the top.
However, the Dons were level on 86 minutes when substitute Revell diverted Murphy’s dangerous delivery past Steele – his second goal in as many games.
Some fantastic defending from Baldock denied Graham after the former Middlesbrough striker got in behind the Dons defence as the game ticked into injury-time.
But, Gomez won it for the hosts in injury-time, stepping up and curling a superb 25-yard free-kick past Cropper after Baldock was adjudged to have fouled Matt Grimes.
MK Dons: Cropper, Baldock, McFadzean, Walsh, Lewington (c); Potter, Forster-Caskey; Bowditch, Williams (Murphy 61), Carruthers (Hall 81); Maynard (Revell 69).
Unused subs: Burns, Kay, Spence, Emmanuel-Thomas.
Goals: Carruthers (36), Revell (86).
Attendance: 12,693 (345 Dons fans).