Luke Shearer thought he had won a penalty early on after tangling with Mark Ross in the area but instead the winger was shown a yellow card for simulation.
Luke Benbow tested Avenue keeper Steve Drench with an almost 30-yard free-kick and the stopper did brilliantly to deny Leon Broadhurst from the resulting corner.
Kyle Perry headed wide in the 19th minute as Stourbridge began to dominate the game and Stuart Pierpoint also saw a header go over.
It took the Glassboys just 4 minutes of the second half to br3eak the deadlock as Shane Killock, under pressure from Perry, flicked a Tom Tonks long throw past his own keeper.
Broadhurst missed a golden opportunity in the 62nd minute, heading over from six yards after Perry nodded Benbow’s ball into his path.
Matt Gould was alert to save well from Oli Johnson before the home side doubled their lead in the 69th minute.
Shearer used his pace to break through a gap in the Avenue defence and he finished calmly past Drench.
Bradford made the final quarter of an hour a nervy one as Adam Boyes rounded Gould and tapped home after the Stourbridge defence were caught off guard.
But the Glassboys' backline stood firm and they almost added a third in the 89th minute as Broadhurst slipped in Perry and the forward’s effort crashed back off the post.
Bradford went close in the 4th minute of added time with an effort that flashed across goal but Stourbridge held on and now look forward to a trip to Avenue`s league rivals Leamington on Saturday, December 16th.
(Photo: Luke Shearer - Gareth Dalley)