Pools had been pegged back for almost the entire game until starting to show some attacking inclination after the break.
Then Ritchie Humphreys curled over a 57th minute cross from the left that Posh midfielder Micah Hyde failed to control, hitting his attempted clearance straight to the feet of Monkhouse, who gave Joe Lewis no chance from a dozen yards.
Danny Wilson then sent on Barker for reported Celtic strike target James Brown and the delighted Pool boss saw the substitute double the lead with his first touch.
While home skipper and Wales international Craig Morgan tried to shield the ball back to England Under-21 keeper Lewis, Barker nipped in to place a shot into the empty net.
Posh dominated the first half with George Boyd a constant threat on the left, while former Wycombe pair Russell Martin and tricky winger Sergio Torres showed great understanding on the opposite flank.
But only Craig Mackail-Smith seriously threatened Pools keeper Arran Lee-Barrett, who stormed off his line to block a fierce shot.
Boyd ensured a frantic finish, pulling one back for Posh with shot low into the right-hand corner of Lee-Barnett's net after a probing Chris Whelpdale cross on 77 minutes.
But Hartlepool, with Michael Nelson prominent, stood their ground although Whelpdale went close with a last-minute header that Lee-Barett turned to safety.