The Posh keeper failed to hold Heckingbottom's near post header in the 52nd minute as promotion-chasing Wednesday came from behind to clinch three vital points.
It was harsh on Barry Fry's side that, despite taking the lead through the lively Wayne Purser, remain second bottom and nine points away from safety.
But they made it hard for Wednesday with Simon Rea, Sean St. Ledger and Richard Logan all being denied by David Lucas.
The struggling visitors began brightly with Logan latching onto a long punt and blazing over and then Purser almost caught Lucas out with a looping fourth minute header.
Wednesday's Glenn Whelan had a goal chalked off for offside moments later and then saw a 25-yard shot saved by Tyler in a lively opening.
Lee Peacock then intercepted Mark Arber's pass and sent Steven MacLean away but Tyler did well to stop the Scottish striker's effort with his legs.
Peterborough struck the first blow in the 20th minute. Lucas failed to hold Simon Rea's header from Curtis Woodhouse's corner and Purser bundled the ball home after a host of Owls players had failed to clear the ball.
Owls were all at sea at the back and Purser, signed from Nationwide South side Hornchurch in November, almost doubled United's lead in the 25th minute only to have his shot saved.
Paul Sturrock's side scored an undeserved equaliser ten minutes before the break when MacLean scored from the penalty spot after he had been held down six yards from goal by Craig Ireland.
Purser then flashed a shot across goal after turning Richard Wood as United refused to be downhearted but after Whelan and Chris Brunt had both been denied by excellent saves by Tyler, the Posh keeper made the crucial 52nd minute error that handed victory to the Owls.