Dack opened the scoring on the half-hour with his 13th of the season, heading over stranded Dons goalkeeper George Long from Jack Payne’s deep cross. The goal was given despite Deji Oshilaja’s attempted goalline clearance.
Tony Mowbray’s side almost extended their lead seven minutes later, as Charlie Mulgrew’s deflected free-kick hit the side netting.
AFC Wimbeldon had chances of their own with Jon Meades and Andy Barcham going close in the opening half.
And they had further opportunities after the break as Lyle Taylor and Harry Forrester went close for the Londoners, who remain just two points above the relegation zone.
However, Blackburn made them pay as Elliott Bennett scored a spectacular solo effort from 25 yards for his first goal since April.
Dack then chipped Long following fantastic play out wide by Danny Graham to earn the visitors their fourth consecutive win.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.