Trailing 1-0 at the break against a side who had won their three previous matches, Shrewsbury stirred themselves and superbly taken goals from Ben Davies and Derek Asamoah allowed them to overcome Peter Gain's first-half strike for Posh.
Going into the game on the back of a ten-match unbeaten record, Shrewsbury made a tentative start and were relived to see a Gain strike in the 11th minute flash past an upright.
Peterborough went even closer two minutes later when Town central defender Danny Hall diverted a cross against his own post and out for a corner.
So it was no surprise when the visitors finally went ahead in the 22nd minute.
Hesitant Shrewsbury defending saw the ball fall to Gain on the edge of the box and he had time and space to pick his spot and score with a low drive.
Shrewsbury could only play better in the second half and, following an early escape when George Boyd crashed a shot against the woodwork, they drew level after a spell of pressure with Davies scoring with a delightful curling shot.
The match turned decisively ten minutes from time as Peterborough's Craig Mackail-Smith saw his angled drive rebound off a post.
Shrewsbury then swept down field where the impressive Asamoah smashed home an unstoppable drive that secured a win that lifts them over Peterborough in the push for the League Two play-off places.