In what was largely a dire display of football, the Tykes defence succumbed to a late sucker punch as the tireless Gary McSheffrey picked out Platt to score his first goal in 46 appearances for the Sky Blues.
To the casual observer, Coventry's first-half performance was not one typical of a side battling for survival.
Keith Hill's Barnsley too, far from guaranteed survival in the second tier, seemed unwilling to demonstrate any cut and thrust throughout a drab 45 minutes.
And it was not until the 17th minute that either side conjured up a meaningful attempt on goal, Alex Nimely making the most of a hefty kick from Joe Murphy to jink into the box. Providing an indication of what was to come, he scooped his tame shot high over the crossbar.
Coerced into some sort of response, Michael Tonge carried the ball into space to test Murphy from 25 yards, but the former Scunthorpe goalkeeper was well placed to parry clear.
Jimmy McNulty soon tried a curling long-range effort of his own but miscued his drive to the right of the target.
The Sky Blues registered their first shot on target shortly before the half-hour mark, Richard Keogh nodding Carl Baker's floated corner into Luke Steele's gloves.
The home crowd's malaise manifested itself in a chorus of groans five minutes before the break as Nimely spurned a golden opportunity to break the deadlock. After craftily sneaking through the Tykes' back line, Steele's kidology paid dividends as the Manchester City loanee pumped his shot harmlessly into the hoardings.
If Andy Thorn had rallied his troops to stamp their authority on Barnsley after the break, it was not immediately in evidence as the second half got off to a lethargic start.
With the hour mark approaching, McSheffrey thought he could beat Steele from distance but Stephen Dawson raced across to cover. The ex-Birmingham striker went closer in the 65th minute, though, making the most of a lofted ball forward to test Steele with a bullet header.
McSheffrey's verve sparked something in the home side and Martin Cranie soon arrived in a good position to ping the ball into Steele's gloves, with Barnsley on the back foot.
Nimely re-emerged as a creative outlet as the final 20 minutes approached, providing a tricky cross that Platt could not manage to direct into the net.
Craig Davies' attempt to unsettle Murphy with a potential daisy-cutter resulted in a harmless hooked shot as the visitors clutched at anything thrown their way.
By now both sides were exhausted by their own profligacy, and a critical lapse in concentration saw Barnsley's defence punished in injury time.
McSheffrey's earlier travails finally paid off as he picked out Platt to nod home what could prove to be a pivotal goal in the Sky Blues' troubled campaign.