Schumacher produced the only moment of quality in a largely dour game in which Swindon should have been home and dry by half-time.
Schumacher was shown the door by Bradford boss Stuart McCall in the summer after being deemed surplus to requirements at Valley Parade, but the former Everton youngster showed Premier League technique in guiding Gary Roberts' crossfield pass past Phil Smith in the Swindon goal.
Earlier Michael Pook had given the Robins the lead with his first goal in eight months after Crewe failed to clear a Sofiane Zaaboub corner.
That goal appeared to signal a potential rout for Town as the Alex rarely looked like getting back into the game.
Zaaboub should have doubled his side's advantage when he took too many touches before blasting wastefully over after being set up by Craig Easton.
Schumacher's wonder goal appeared to leave Swindon shell-shocked as they came out for the second half and despite long periods spent flinging crosses into the area, they failed to make a significant breakthrough.
Neither goalkeeper was troubled in 45 minutes of sheer tedium which failed to match the excitement of the opening period.
For the last 15 minutes Paul Sturrock's side resorted to flinging long balls towards Lee Peacock in the hope of feeding off the scraps left behind.
Only once did this prove fruitful, but Pook's late half-volley was well saved by Ben Williams.
Crewe substitute Chris Dickson then nearly grabbed a late winner as he was allowed to run at the Swindon defence, but his low left-foot effort was well kept out by Smith as both sides settled for a point.