The Glassboys had the ball in the net after 4 minutes when Ashton keeper Paul Phillips appeared to drop the ball into his own net, only for Josh Craddock to be penalised for a foul on Phillips.
The visitors took a 12th minute lead when a high ball into the Stourbridge penalty area was headed on to the unmarked Philip Marsh who had time and space to lob the ball over Dean Coleman and into the net.
Stourbridge struggled to find a final ball for much of the half but began to exert more pressure in the later stages, with Reece Hales and Ben Billingham going close with headers, and then Hales putting a low cross in which no Glassboys player could get on the end of.
The early stages of the second half were marred by an injury to Stourbridge skipper Billingham, after a clash of heads saw him knocked out. After lengthy treatment, and despite a stretcher being called for, Billingham was able to walk off gingerly, with Brian Smikle replacing him.
The Glassboys struggled to make any impression on the Ashton defence for much of the second half, and the quality of the match left something to be desired for a while. The closest either side came to scoring was a speculative lob from Richard Bennett which almost caught out the back-pedalling Coleman who did well to tip it over for a corner.
However, Reece Hales sparked proceedings into life 14 minutes from time, shaking off the attractions of a defender before firing a volley over Phillips and into the roof of the net from 20 yards to level the scores.
Thereafter Stourbridge forced a number of corners but were unable to make any real chances other than shots from distance which were for the most part off target. At the other end, Ashton threatened on the break, and Coleman had to be alert to push a swerving shot from Martin Pilkington.
The point means that Stourbridge remain in 9th place in the Evo-Stik League Premier Division table, 3 points and four places off the play-off positions.