Peterborough had enough chances to have put the game out of Town's reach in the opening 30 minutes, but the stand-out performer was once again teenage keeper Joe Hart who produced another inspired display.
The England Under-19 star gave a hint of what was to come with the early denial of Danny Crow before the same player grazed the visitors' crossbar with an effort from longer range after beating Richard Hope.
The lively 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 minutes before the break, Hart underlined his potential by diving to his right and making a superb reflex save from James Quinn.
Apart from forcing a couple of corners in the first few minutes and an effort by Jamie Tolley on 21 minutes that sailed wide, Town showed little attacking threat in the first half.
A half time tactical change saw Town match their hosts' formation, with Duane Darby and Jay Denny entering the fray.
And the changes soon paid dividends, a misplaced clearance by Posh's Sagi Burton was picked up by Darby who fed Ben Herd and he swept the ball into the penalty area where Sorvel fired past Mark Tyler for his first Town goal.
In reply, Posh boss Mark Wright introduced new wide players Ryan Semple and David Farrell, and they increased the pressure on the Shrewsbury goal. 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 former Town loanee Richard Logan's effort to be correctly ruled out for offside.
And two minutes later the game was over, Shrewsbury made sure of the points after substitute Darby netted after a smart turn. He had been fed from the left by the otherwise quiet Colin McMenamin.
It was something of a smash and grab by Town, after Posh had 27 shots to the visitors' four, but the most important statistic was tha Shrewsbury left with three points.