A poor first half saw the Bantams edge possession but neither goalkeeper had a real save to make.
Christy Pym was firmly behind a low shot by Clarke Oduor after 17 minutes for a routine stop.
And it took a fine last-ditch tackle by Lewis Brunt just before that to stop Tyler Smith pulling the trigger six yards out as Mansfield struggled to clear a corner.
Immediately after the restart, Smith forced Pym to dive to his right to grab his rasping half-volley.
Harry Lewis finally had work to do after 56 minutes as he kept out Davis Keillor-Dunn’s powerful strike, diving to his right.
Eight minutes later Ollie Clarke poked a loose ball just wide after a Keillor-Dunn shot was blocked.
Lucas Akins almost broke the deadlock 11 minutes from time, but his glancing near-post header from a corner sailed across goal and hit the base of the far post.