The Cheshire side had lost all four games under caretaker boss Neil Baker since long-serving manager Dario Gradi underwent heart surgery last month.
But Gradi's assistant was relieved for small mercies after picking up his first point in charge, but really Crewe should not have left the struggling visitors off the hook.
After a dismal first half, Crewe came out for the second period firing on all cylinders and scored twice within the first three minutes of the second period.
Steve Jones showed a fine finish to take the ball away from two Bradford defenders and round keeper Marlon Beresford before slotting in from an angle.
Then two minutes later, Dean Ashton deposited a thumping header down in to the corner of the net after David Wright had crossed the ball into the box.
Both Crewe strikers could have scored again within a couple of minutes with Ashton firing over and Jones being denied by Beresford's body.
But Bradford midfielder Paul Evans executed a brilliant overhead kick after David Wetherall had nodded back a corner and home keeper Clayton Ince was beaten all ends up.
That 55th minute strike was just the tonic Nicky Law's men needed for they had been marginally the better of two poor sides before the break.
They regained their dominance and Crewe were forced to defend in depth against the tricky wing play of Ben Muirhead and Nicky Summerbee.
Ince saved a point-blank header from Tom Kearney on the hour mark and Andy Gray fired over from inside the six-yard box as Bradford edged closer to an equaliser.
It duly arrived in spectacular fashion like their first when Muirhead hit a swerving volley from 20 yards that caught the top corner of the net beyond Ince's reach.