The tall frontman was brought on for leading scorer Shefki Kuqi who was dropped to the bench and he came up trumps when he slid in to scramble home the Owls leveller nine minutes from time.
With the prize of first division survival in their sights Bradford had begun in determined mood and striker Ashley Ward almost opened their account inside two minutes.
The City frontman charged forward from halfway before letting fly with a 30-yard drive, but his effort rattled the Wednesday bar and bounced to safety.
Ward, who has only hit the net once this year, looked most likely to break the deadlock and he was unlucky again when a far-post header flew inches wide.
Wednesday's reshuffled attack rarely threatened in the early exchanges as Bradford defence was well marshalled by their skipper David Wetherall.
Crane hit a weak shot at keeper Aidan Davison and strike partner Lee Bradbury saw a long-range drive fly over the bar.
Bradford's enterprise deserved a goal and Claus Jorgensen's surging run was rewarded when the assistant referee flagged after he was knocked out of his stride by Bradford old boy Ashley Westwood.
City's top marksman Andy Gray stepped up to coolly slot home a right-foot spot-kick which sent Owls keeper Paul Evans diving the wrong way to his right.
Injury-plagued midfielder Simon Donnelly was introduced at half time after a four-month lay-off and with his first touch he hit the foot of a Bradford post with a curling 20-yard shot.
The Owls mounted a fierce second-half fightback, but could not find a way through until midfielder Jamie Lawrence was show a red card for a second bookable offence.
From the resulting free-kick Bradford's depleted defence was at sixes and sevens and after Dean Smith's header rebounded off the bar Crane was on hand to force home his fifth goal of the season from inside the six-yard box.