Two goals from Jordan Fitzpatrick and a late Ben Billingham penalty secured the win against a Market Drayton Town outfit that battled hard for every ball.
With Reece Hales denied permission to play by his parent club, Kidderminster Harriers, Josh Craddock made his debut second time around in attack alongside Luke Benbow, who had passed a late fitness test.
Stourbridge controlled the early stages, but it was the home side that took the lead from their first attack, Paul McMullen rising unopposed to head home a right-wing corner beyond Dean Coleman.
To add injury to insult, Brian Smikle replaced Benbow before the game could restart, the Glassboys striker having felt a twinge from his Hamstring strain.
Ben Billingham almost embarrassed the home keeper, his shot straight from the resulting kick-off only just clearing the crossbar, and the same player should have done better when firing over the bar shortly afterwards.
For a while it looked as though it might be "one of those days" but just past the half hour mark, Jordan Fitzpatrick stole in at the far post to place a firm header into the net from Leon Broadhurst's cross.
And it was Fitzpatrick who put the Glassboys ahead on 58 minutes with a precise shot from the edge of the area that seemed to deceive the home keeper.
Stourbridge could have added further goals but it was the home side that came closest with a close-range effort striking the bar before Billingham was tripped in the area when well-placed to shoot. With the reliability of Sean Geddes from 12 yards no longer on call, Billingham himself took the spot kick and fired low into the left-hand corner to make the game safe, despite the keeper getting a touch.