Platt's late strike and Izale McLeod's close-range finish extended the Dons' unbeaten home league run to seven games after Andy Booth's first-half opener for the Terriers.
Milton Keynes Dons had marginally the better of a dour opening as both teams struggled to come to terms with a gale force wind.
But just moments after he had come close with another effort, Booth brought the game to life when he found space to open the scoring for Huddersfield on the half-hour mark.
The veteran striker was left unmarked just eight yards out to glance home his sixth goal of the season from Nathan Clarke's long free-kick.
Milton Keynes were level just two minutes later though, when McLeod turned in his 15th of the season from close range.
Paul Mitchell's clever ball put Ben Harding clear, and when his effort was saved by Huddersfield keeper Paul Rachubka, McLeod was on hand to slot home the rebound.
More good work by McLeod gave Harding a glorious chance to put the Dons ahead just before the interval, but he fired wide left-footed from 15 yards.
And then Platt headed just over for the home side after beating Rachubka to a long punt, before being clattered by the Terriers stopper.
But if Platt was unlucky on that occasion, he should have done better in the 60th minute when a defensive error put him clear on goal, only to hesitate and allow Clarke to get in a last-ditch challenge.
At the other end, sub Pawel Abbott looked to have grabbed the winner for the visitors 11 minutes from time but his header from Lee Fowler's corner was ruled out for offside.
Abbott was booked for protesting after fellow sub John McCombe was flagged.
But after the inspired Abbott had come close again with a drive that fizzed just over the bar, Platt stole the points for the Dons two minutes into stoppage time when Tom Clarke's defensive header fell kindly for him eight yards out.