Carlisle hearts were broken deep into time added on at London Road as Christian Burgess looped a perfect header into the back of the net just as it appeared that the visitors had done enough to earn a replay.
The game took a while to get going but a Taylor free kick on 5 minutes brought a wild swing of the leg from Vassell. He failed to make a connection but Newell recovered it on the edge of the box and his cross to the back stick had to be cleared behind by Dempsey as it caught on the wind and threatened to creep in.
The Cumbrians drew first blood with their first attack of the day when Alnwick and Smith hesitated as a high ball bounced awkwardly on the edge of the area. Lively striker Derek Asamoah didn't need to be asked twice and he nipped between the pair to register goal number three of the campaign with the cheekiest of chips into the empty net.
The home side tried to respond but shots from Taylor and Newell lacked conviction as Carlisle worked hard to close the gaps. A purposeful run from Taylor caused problems as Peterborough stayed forward and he left two in his wake as he burst through with a clear sight of goal. Bostwick stood and waited but he let one fly as the ball rolled into his path and it needed a one handed save from Hanford to send it away from the bottom corner.
The visitors held their shape and they almost doubled their lead when Robson released Grainger on the overlap. He cut inside his marker and was a whisker away as he drilled a right footed shot just past the post.
And Carlisle went even closer just moments later when Robson curled a superb free kick delivery into the box. Meppen-Walter watched it skim the heads and he wheeled away in disappointment as his volley bounced past the target with Alnwick well beaten.
The home crowd started to turn on their team as they grew wasteful in possession and Sweeney was next in line to test the stopper when he asked for a pass from a long run from Dempsey. He was caught in two minds as his 22-yarder fell nicely for the Posh stopper.
Peterborough saw more of the ball as half time approached and Taylor did well to cut it back as he jinked in from wide. Bostwick was unmarked but he went for power and succeeded only in side swiping the ball towards the corner flag.
A corner from nothing brought Peterborough back on terms when Newell sent his delivery onto the penalty spot. Christian Burgess used his size and strength to make sure he got the connection which took it into the roof of the net.
It was end to end through the closing stages of the half and United thought they'd restored their lead when Grainger placed the ball for a 25 yard free kick. It flicked off the top of the wall and Alnwick had to move across quickly to tip it over his bar.
A willingness to keep going took Robson through three bodies after the break and he brought the save of the day from Alnwick as he dug the ball out of his feet and let one fly. It appeared to be going in until the stopper somehow arched his back and scooped it over the bar.
Taylor was a constant outlet and he set off on another run which brought a clip on his heel from Grainger. He stayed on his feet and poked a poor shot into the side netting.
Robson saw plenty of the ball at the other end and he fizzed an early cross across the face of goal as Sweeney slid in. He was an inch away from getting the touch it needed.
Good work from Washington created an opening at the other end as the pace of the game quickened and it was Mendez-Laing who almost made the difference when he nicked a loose ball off Dempsey's toe. He took a touch and rifled a left foot shot through bodies but Hanford was well placed to deal with it.
Potts cut inside to have a shot deflected away for a corner as United bit back, but they had to stay focused at the other end as the hosts started to throw men forward. They held their shape well and the best Posh could muster from a ten minute spell of keep ball was a miscued effort from Bostwick.
Taylor showed a good turn of skill as the clock ticked down when he rolled his man inside the area. Hanford saw it late but he reacted well to beat it away.
Peterborough kept the pressure on and they made their only clear cut chance of the closing stages count when Burgess doubled his tally for the day with a perfectly looped header into the back of the net.
Peterborough - Burgess (42, 90)
United - Asamoah (8)
Peterborough - Vassell (45)
Peterborough United - Alnwick, Smith, Newell, Burgess, Santos, Taylor, Payne, Bostwick, Mendez-Laing (Otzumer 66), Washington, Vassell. Subs - Henry, James, McEvoy, Ferdinand, Anderson, McCann.
Carlisle United - Hanford, Brown, Anderson, Meppen-Walter, Grainger, Potts, Sweeney (Beck 90), Dicker, Dempsey, Robson (Amoo 75), Asamoah (Kearns 87). Subs - Eccles, Paynter, Brough, Iliev.
Referee - Mr Scott Mathieson
Attendance - 3,168 (214 away fans)