Substitute Kayelden Brown could not convert Darragh Bustin’s hopeful hook into the box, Kieran Morris’s far-post header from a corner got pushed around the post by keeper Alex Tokarczyk and then Bustin somehow scooped over the bar from a yard out at the death.
The visitors certainly earned their share of the spoils despite barely crossing the halfway line in the second half, losing impetus when creative spark Harrison Crawford was withdrawn through injury at half-time.
Stourbridge started well with Darryl Knights peeling free to whack the near post with a first-time hit from a clever corner routine, while Bradley Wadkins spurned a great opening for the visitors, scuffing when free at the near post from Jack Wood’s cutback.
Both teams showed attacking intent without cohesion until the dying embers of the first half when Crawford sent a dipping 20-yard shot narrowly wide from the left corner of the box and then did likewise from the centre circle with Charlie Price off his line.
Birch’s drive from distance drew a flying stop from Tokarczyk who also had to parry into the air from the midfielder's near-post blast within 90 seconds of the second half starting.
Richard Peniket cleared the crossbar from in front of goal just before the hour and Jordaan Brown’s downward header was almost scrambled in by substitute Alex Nicholls only for the striker to give away a foul as he stretched.
Birch and Martin Riley misdirected efforts during the home side’s late push but far better openings were wasted in Stour’s final flurry.
Glassboys: Price, J Brown, Bustin, Fletcher, Morris, Riley, Knights, Deeney (O’Hanlon, 70), Peniket (K Brown, 70), Birch, Landell (Nicholls, 60).
Unused subs: May, Derrick.
Attendance: 600 (sell out).