But the Stags might have claimed a vital victory if leading scorer Michael Boulding had not seen his first-half penalty well saved by the diving Donovan Ricketts.
The Bantams, however, could also point to a fine first-half display in which they created a hatful of chances, with pacy winger Omar Daley crashing a drive against the post.
Former Stags striker Barry Conlon almost made an immediate impact against the club which showed him the door last summer.
His fierce low drive on the end of a Daley deep cross inside the first minute was superbly beaten away by the diving Carl Muggleton.
From the resulting corner, Kyle Nix's close-range effort bounced well wide with the home side struggling to clear.
Then in the tenth minute, Conlon again went close, curling his finish from 12 yards narrowly past the upright after Guylain Ndumbu-Nsungu's cross caused havoc in the home defence.
The Stags, unchanged for the third successive game, finally posed a threat when Lee Bell's long 19th minute pass released Rory Boulding inside the area.
And when David Wetherall tugged back the young striker, Mansfield were controversially awarded a penalty.
But Michael Boulding squandered the chance to register his 14th goal of the season as his low spot-kick was easily saved by the diving Ricketts.
In a thrilling first half, City hit back immediately when Daley latched on to a loose ball and crashed a close drive from an acute angle against the foot of the post with Muggleton beaten.
Mansfield were defending resolutely against waves of attacks, but in contrast City's rearguard gave the lightweight home attack glimpses of goal.
And from one error, Rory Boulding's deflected shot was only held at the second attempt by Ricketts.
Ricketts made amends with a well-timed save at the feet of Michael Boulding in the 39th minute as the striker threatened to round the keeper and score.
Mansfield full-back Dan Martin was perhaps fortunate to escape a red card in the 53rd minute for a reckless challenge on Daley which sparked a melee involving many players.
Rory Boulding thought he had scored in the 65th minute, but Micky Boulding had already been flagged for offside.
At the other end, Matt Clarke's surging run into the area ended with a fine clearance by Jake Buxton before Mansfield substitute Simon Brown pulled a late chance wide.