The Glassboys made a bright start, with both Luke Benbow and Reece Hales denied in the opening minutes by visiting keeper Hakan Burton. Benbow in particular probably should have done better when one-on-one with Burton.
However, Curzon established themselves in the game and deservedly took the lead on 27 minutes through Niall Cummins, who turned a low left-wing cross past Dean Coleman from close range.
Stourbridge applied some pressure nearer the break and Will Richards was denied by another fine save by Burton before the keeper got down to parry a shot from Jordan Fitzpatrick.
However, there was more bad news for the Glassboys just before the interval when Benbow, who had looked lively after missing the midweek match at Barwell, crumpled in a heap and had to be helped off with what looked like a recurrence of his hamstring trouble.
Stourbridge upped the tempo in a second half of few real chances at either end, but couldn't find a way past a well-marshalled Curzon defence. Brian Smikle, who had replaced Benbow, couldn't get his shot on target from Richards' knock-down, whilst Burton came off his line to collect any high ball into the box.
Josh Craddock, also on as a substitute, came closest to an equalisr when his 87th minute shot on the turn thumped off the crossbar, with the same player firing over from the rebound as Stourbridge looked to pile on the pressure.
However, Curzon saw out the closing minutes with little further alarm.