Peterborough had enough chances to have put the game out of Town's reach in the opening 30 minutes, but their stumbling block was teenage goalkeeper Joe Hart who produced an inspired display.
The England Under-19 shot -topper gave a hint of what was to come with an early denial of Danny Crow before the home livewire grazed the visitors' crossbar with an effort from longer range after spinning away spinning away from marker Richard Hope.
Crow also set up Adam Newton who should have done better than firing into the side netting - and just when a goal did look on the cards four minutes before the break, Hart underlined his potential by diving right to make a superb reflex save from James Quinn's fierce shot.
Apart from forcing a couple of corners in the first four minutes and an effort by James Tolley on 21 minutes that sailed wide, little was seen of Shrewsbury as an attacking force until they struck decisively 10 minutes into the second period.
A misplaced clearance by Posh's Sagi Burton was picked up by Ben Herd and he swept the ball into the penalty area where 32-year-old Sorvel was ideally placed to fire past Mark Tyler.
With Posh boss Mark Wright successively introducing wide players Ryan Semple and David Farrell, pressure on the Shrewsbury goal was soon resumed but the best was still to come from Hart, the youngster twisting in the air to palm a Semple shot from beneath the bar and behind for a corner.
Posh did have the ball in the net on 81 minutes only for Richard Logan's effort to be ruled out and two minutes later Shrewsbury made sure of the points with substitute Darby netting after good work by leading scorer Colin McMenamin.