Bradford came away from Darlington with a 1-0 win but only their poor finishing prevented the division's bottom side being on the end of another hiding.
The Quakers appear to be dead and buried at the foot of the table as manager Steve Staunton continues to look for a solution to their plight.
Staunton made five changes from the side thrashed 4-0 at Notts County midweek and it showed as City took control of the game from the start.
After dominating the opening stages of the game and going close through Michael Boulding on five minutes, Scott Nielson after 10 and Lee Bullock a minute later, it was no surprise when Bradford took the lead in the 23rd minute.
Steve Williams connected with a Nielson corner to beat Darlington keeper Nick Liversedge with a stooping header at the far post.
The second half saw Bradford squander yet more chances.
James Hanson headed wide from a good position on the hour and then Simon Whalley sent a crisp low drive straight at the Darlington keeper three minutes later.
Bradford keeper Simon Eastwood was briefly called into action in the 72nd minute when Quakers substitute James Collins fired low at the near post.
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