The Stags won this dour encounter with a goal in each half from Derek Asamoah and Adam Murray to record their first win in 11 matches, just 24 hours after finally dismissing manager Keith Curle.
Peters was forced to make two changes after the stormy draw at Chester last Saturday, with the red cards shown to Darren Moss and Martin O'Connor ensuring they will sit out the hectic Christmas period. The Shrews boss recalled Jake Sedgemore and handed a first start to former Port Vale centre-half Liam Burns.
Despite an encouraging start for the home side, during which striker Luke Rodgers was inches away from netting his first goal in 13 games, it was Mansfield that took the lead - scoring against the run of play after 22 minutes.
Asamoah won a tackle from Shrews defender Trevor Challis and cut inside to drill a shot beyond Scott Howie at his near post.
Booed off at half-time things got a little better for the home side after the break, and Challis, Jamie Tolley and Ryan Lowe all brought saves from Stags goalkeeper Kevin Pilkington.
Shrewsbury's best chance of an equaliser fell to Burns - but he blasted over from six yards.
It proved costly as with 16 minutes remaining, Murray put the issue beyond doubt - netting from close range after Shrewsbury substitute Kevin Street slipped when trying to clear.