Carlisle made much of the early running with strikers Joe Garner and Lee Miller both close to a breakthrough.
Garner, in his final appearance of a productive loan spell from Watford, fired narrowly wide from 20 yards before Miller just failed to hit the target with a clever near post flick.
Shrewsbury carried little threat until they moved ahead against the run of play in the 22nd minute.
Good awareness from Luke Rodgers picked out Jon Taylor and the little winger steadied himself before rifling an unstoppable shot high to the far corner of the net from the edge of the penalty area.
Carlisle responded strongly and were level 11 minutes later as Liam Noble, well found by Chris Chantler, drove a low shot from 15 yards to the bottom corner of Chris Weale's net.
The Cumbrians also started the second half brightly with Matt Robson drilling a fierce shot just wide while Noble fired straight at Weale when he might have done better.
But it was Shrewsbury who claimed victory to add to Carlisle's recent struggles in the 64th minute.
Marvin Morgan's half blocked shot fell the way of Parry and the winger did well to hook in a right-footed volley from eight yards to seal a fifth win of the season for Graham Turner's relieved side.