Posh had not won at home since August but goals from strikers Trevor Benjamin and Danny Crow sealed a third successive victory for Keith Alexander's men after successive victories at Stockport County and MK Dons on the road.
Ben Davies did provide a late scare as he smashed home a penalty for Shrewsbury, but the visitors were unable to find the all-important leveller in a frustrating end to the match.
Shrewsbury had in fact began the brighter of the two sides and missed a string of chances before Posh broke the deadlock.
Andy Cooke headed an effort straight at goalkeeper Mark Tyler, Richard Hope nodded a couple of set-pieces wide and Derek Asamoah saw a fine volley diverted over the crossbar.
Town were made to rue those missed opportunities and were punished three minutes before half-time when Benjamin smashed in an unstoppable header at the back post after Adam Newton had raced down the right-hand touchline and delivered a deep cross to the leading goalscorer.
Shrewsbury began the second period eagerly but were caught out with 64 minutes on the clock when a corner was cleared to Peterborough teenager Crow on the halfway line.
Crow, who finished last season as the club's top-scorer, surged his way through the Town half and although Hope got himself in the way of his initial shot, he kept his cool to slot the ball past keeper Chris MacKenzie.
Town boss Gary Peters responded with a series of substitutions and eventually found a way through when the lively Davies was felled in the box by Peter Gain with nine minutes remaining.
Davies dusted himself down before smashing an unstoppable penalty into the top corner giving Tyler no chance.
Town pressed on in search of an equaliser with the industrious Asamoah attempting to jink his way through the home defence, but they were resigned to only their third defeat of the season.
Meanwhile, Peterborough appear to be on the up following their indifferent home form in September.