The luck was against the gutsy Stags as the deadlock was broken five minutes into the second half. Mark Ellis’ cross from the right took a deflection that lifted the ball up and over goalkeeper Lenny Pidgeley and half-time substitute Tyrone Barnett made sure it went in from almost on the line.
A tight first half had seen teenage midfielder Jack Thomas twice go close for the hosts.
After 25 minutes he was just too high with a lob from outside the box and in the 39th minute his long range blast forced Jayson Leutwiler to get down to his left to save.
But there were few other chances as an enthralling half ended in stalemate in the bright Bank Holiday sunshine.
After the early breakthrough goal, Shrewsbury spent much of the rest of the second half defending against constant Mansfield pressure.
But, apart from a Chris Clements shot that whistled over the crossbar, the visitors’ keeper was well protected.
It was a fifth straight win for the Shrews but a fourth defeat on the bounce leaves the Stags still in the relegation battle.