The Dons were frustrated for 66 minutes by their opponents before a bizarre opener by another sub, Dean Bowditch, opened the floodgates and they remain a point off an automatic promotion place.
MK Dons needed a huge slice of luck to go ahead as Andy Butler’s attempted clearance off Baker’s cross came off Bowditch, who had only been on for two minutes, and dropped into the net.
Goalkeeper David Martin then preserved his side’s advantage when he tipped over Richie Wellens’ half-volley from the edge of the area.
But the hosts doubled their lead when Dele Alli found Baker in space on the right and he worked his way closer to goal before blasting his shot past Stephen Bywater.
The Dons had a third and Baker his second with five minutes left when he shot across goal and into the bottom corner after again being found by Alli