Peter Murphy struck near the end of the first half to decide this lively, often entertaining encounter, during which Shrewsbury often held the upper hand and will reflect on a succession of near misses, particularly during the opening half hour.
Skipper Ben Davies, Kevin McIntyre and Grant Holt could hardly have gone closer as the League Two outfit forced Carlisle to defend deep inside their half.
With both sides buoyant after fine results on the opening day of the season, Shrewsbury 4-0 winners over visiting Macclesfield and Carlisle triumphant 3-2 at Bristol Rovers, each team quickly settled to the task and produced some crisp exchanges.
Davies forced Carlisle 'keeper Ben Williams into a diving save, while at the other end Marc Bridge-Wilkinson sent a low drive narrowly wide. Carlisle threatened again through Danny Carlton, while McIntyre saw his shot flash past the visitors' upright.
It was in the 35th minute when Shrewsbury came closest to breaking the deadlock. Full-back Ben Herd escaped down the right and sent over a fine cross that was met perfectly by Holt, but the big front man could only watch in frustration as his half-volley rebounded back off the post with Williams beaten.
Four minutes before the break, however, Carlisle struck decisively. After Danny Graham was fouled on the edge of the box, up stepped Murphy to curl home a sweetly struck free-kick.
After the break Shrewsbury, managed by Carlisle-born and former Brunton Park boss Paul Simpson, pressed hard for a leveller and despite several spells of intense pressure found the Carlisle defence in resolute mood.
With 12 minutes remaining centre-back Mike Jackson almost drew them level, but headed wide after a Davies free-kick had come back off the bar, while the visitors' best chance of the half came right at the death when Bridge-Wilkinson shot just wide with a curling effort.