The Scottish goalkeeper was making his first start in two months after Alex boss Steve Davis shook up his side following back-to-back defeats. Among his six changes was the axing of regular number one Steve Phillips.
Martin rose to the occasion when he stopped Hanson's header flashing into the bottom corner to keep the Railwaymen in contention under heavy Bradford pressure.
Manchester City youngster George Evans was handed his senior debut in the home ranks and the midfielder provided Crewe's biggest threat in the first-half when his right-footed blast from 25 yards forced an unconvincing parry from Bradford keeper Jon McLaughlin.
Max Clayton and Chuks Aneke provided tame efforts on goal for the hosts and it was Bradford who looked more potent with the fit-again Nahki Wells back in the attack alongside Hanson.
But both frontmen wasted decent first-half chances with Hanson lofting over inside the box and Wells dragging his shot wide after he had been sent clear by Nathan Doyle.
Hanson had his head in his hands soon after the restart when he scuffed an even more presentable opening past after the ball had dropped conveniently into his path eight yards out when Wells' initial shot was blocked.
Bantams' keeper McLaughlin showed good reactions to palm Harry Davis' curling free-kick around the post.
But Martin's save was even more impressive when keeping out Hanson's header from a James Meredith cross.
Crewe substitute Brad Inman went close to grabbing the winner when his late curler slipped just past the far post.
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