Hatch had been on the pitch only eight second-half minutes after replacing Chris Whelpdale before storming forward to let fly with a 73rd minute shot that took a deflection off Barnet skipper Ismail Yakubu on its way into the roof of the net.
Despite stretching five across the middle in a bid to stifle the supply to Posh's free scoring frontmen, Barnet still managed to create early openings for their own lone striker Cliff Akurang.
The 26 year-old New Year signing from Blue Square Premier outfit Histon tested Joe Lewis from 20 yards and saw two other efforts deflected behind for corners.
Posh tended to be muscled out at the other end although Joe Devera did well to get his body in the way of a fierce drive from Craig Mackail-Smith and Max Porter cleared off the Barnet line when Mackail-Smith twisted his way past three defenders and goalkeeper Rob Beckwith.
Beckwith saved well from Dean Keates, pushing a header round the post, as Posh tried to up the pace after the break yet Barnet still threatened with Albert Adomah forcing Lewis to save at full stretch with Kieron St Aimee also going close.
Mackail-Smith burst forward to fire into the side netting before Yakubu scrambled a header from McLean off the Barnet line and although powerless to prevent Hatch's winner, Yakubu denied his former team-mate a second when he somehow headed the ball out from under the crossbar.
But while Posh are now six games unbeaten, Barnet were condemned to their fourth successive single goal League Two defeat.