Platt pounced from close range in the 63rd minute to end plucky Rovers' resistance, after Lloyd Dyer's sizzling free-kick had broken the deadlock at the National Hockey Stadium.
Dons boss Martin Allen named the same line-up that won 2-1 at Macclesfield last Saturday, while Junior Agogo - on the verge of a move to Nottingham Forest - was left out of the Rovers squad altogether.
Rovers dominated the early play and Lewis Haldane was denied by Dons' goalkeeper Adolfo Baines from close range in the 11th minute, after Baines had flapped at Andy Sandell's long throw.
Aaron Wilbraham should have put the Dons ahead on the counter-attack three minutes later after Platt's flick had been saved by Pirates' keeper Steve Phillips, but he somehow sliced the rebound wide of the open goal from three yards.
But the Dons didn't have to wait long to take the lead as Dyer's superb 30-yard free-kick put them in front on the half hour mark.
Dyer gave goalkeeper Phillips no chance by whipping the ball emphatically over the wall and into the top corner, after Izale McLeod had been brought down by Byron Anthony on the edge of the box.
Milton Keynes settled into their stride after the goal and Drissa Diallo headed Jon-Paul McGovern's searching free-kick into the side netting at the far post in the 39th minute.
McLeod toe-poked just wide five minutes after the break from Dyer's incisive pass as the Dons burst out of the blocks in the second half.
Sandell wasted a good shooting chance for Rovers a minute later when he dragged his effort badly wide from the edge of the box as the Dons' defence backed off.
And Platt grabbed his second goal in two games to put the Dons 2-0 up from close range in the 63rd minute.
Pirates keeper Phillips got a hand to Smith's angled drive but as the ball spun up it was headed off the line by Aaron Lescott into the path of Platt, who headed it straight back into the net from five yards.
Dyer almost made it 3-0 when he skinned Craig Hinton in the 82nd minute, but his angled drive was well saved by Phillips.