Caretaker boss David Wetherall had hoped for some beginner's luck as his Bradford side looked to ease their relegation fears, but Crewe's Ryan Lowe piled on the misery with a late winner.
The Bantams had already enjoyed two amazing escapes with Alex's ace marksman Luke Varney missing a couple of gilt-edged chances, but the highly-rated striker made amends two minutes from time.
After 40 games without a goalless draw, the Railwaymen looked to be heading for a point until Varney picked out Lowe with a composed pass and the midfielder drove his low right-foot shot beyond keeper Donovan Ricketts from 12 yards out.
It was cruel on Wetherall and City, who have now failed to win in their last six games, but in truth the visitors looked the more likely to score as the game wore on.
Wetherall was given a standing ovation before the match and he could have had a dream start after just four minutes but midfielder Steven Schumacher side-footed wide from six yards.
Crewe responded with some neat approach play and Varney should have done better when Lowe sent him clear after 14 minutes.
The Crewe striker looked odds to add to his 23 goals this season but Ricketts did well to block his shot with an out-stretched hand.
City's most potent threat came through young winger Joe Colbeck and Crewe keeper Ben Williams had to stand up well to push out his fierce drive.
City had plenty of possession without creating too many openings and after the break Crewe looked more likely to break the deadlock.
Full-back Jon Otsemobor tested the City defence with some surging runs down the right and only an offside flag denied Rodney Jack after 61 minutes.
Ten minutes later Otsemobor was again the provider with another teasing cross into the six-yard box but, with the goal at his mercy, Varney got his feet in a mess and failed to make contact.
City responded with a curling shot from midfielder Marc Bridge-Wilkinson but his effort flew wide and the home side were sunk by Lowe's late strike.
Varney showed his quality by picking out his team-mate with a neat pass and Lowe kept his head to drill his shot beyond the exposed Ricketts.