The Dons started well and skipper Keith Andrews lashed just wide from 22 yards in the second minute after bursting past three defenders on the edge of a crowded box.
Shrewsbury battled back and Ben Davies' curling 30-yard free-kick was gathered at the second attempt by Dons' on loan Northampton goalkeeper Lee Harper, before Dave Edwards headed Davies' teasing cross over when well placed in the eighth minute.
But Milton Keynes regained control and Martin Allen's side totally dominated the rest of the first half.
Sean O'Hanlon headed Jon-Paul McGovern's pin-point free-kick straight at Scott Shearer and McGovern's 25-yard volley was well saved by the Shrews' keeper before Edds' emphatic 28th minute half-volley put the Dons in front.
Edds perfectly controlled Platt's knock-back after a mix-up between Shrews' defenders Sagi Burton and Gavin Cowan and lashed a fierce low strike into the corner from the edge of the box.
Izale McLeod was denied three times by busy Shrews' keeper Shearer before he set up Platt superbly for the Dons' second goal in the 58th minute. McLeod skinned Shrewsbury defender Kelvin Langmead down the left before standing up a fantastic cross to the far post that the unmarked Platt easily headed past Shearer from close range for his sixth goal of the season.
At the other end the unmarked Edwards missed a great chance to put the Shrews back in the game when he headed Davies' cross badly over from eight yards.
But the Dons continued to dominate and the fired-up Platt lashed a rasping half-volley just wide of the top corner after swiveling on the edge of the box, before McGovern headed Dyer's corner badly wide from close range midway through the second half.
The Shrews piled on the pressure in the closing stages in search of a lifeline but the stretching Stuart Drummond wasted their best chance when he blazed over when well placed.