The towering striker, who along with Izale McLeod was compared to a pub striker by Danny Wilson on Saturday, headed the winner to give Dons their first victory in 12 matches.
Wilson made two changes to the team that lost 3-2 at Blackpool, with Gareth Edds and Malvin Kamara coming in on the right for hamstring victims Trent McClenahan and Wade Small.
Milton Keynes had the better of the early exchanges and Platt forced visiting goalkeeper Paul Musselwhite into a fifth minute save with a header from Edds' deep cross.
McLeod nipped in on the end of Platt's flick in the 10th minute but was denied by a reflex stop from Musselwhite, before on-loan Sheffield
United youngster Stephen Quinn curled a 35-yard effort inches wide.
At the other end, Wayne Corden skinned Edds but his fierce 20-yard strike was tipped around the post by Matt Baker.
And as Scunthorpe battled their way into the match, Billy Sharp capitalised on some poor positioning by Dean Lewington to burst away and beat last man Pablo Mills only to strike it straight at Baker.
But Dons regained control and after Quinn again went close with a drive from the edge of the box that Musselwhite tipped round the post, Platt broke the deadlock in the 43rd minute with a near post header from Nicky Rizzo's corner.
Moments later Kamara slotted McLeod away but was he was prevented from doubling the lead by a superb last-ditch tackle by full-back Nathan Stanton.
Dons had the better of a scrappy second half and went close to doubling the lead through Quinn's stretching strike from long range which almost caught out Musselwhite.
The Iron offered very little in a strangely subdued second-half performance against the rock-bottom Dons.
And the only time they tested home keeper Baker after the break was through Ian Baraclough's fizzing 25-yard free-kick that was easily saved as the Dons climbed off the foot of the table at the expense of Swindon.