Kevin McDonald fired the hosts into a 1-0 half-time lead with seconds remaining in the first half, with Nouha Dicko later doubling the advantage to ensure that Kenny Jackett's men move ahead of Leyton Orient, who succumbed to a last-gasp 2-1 defeat away to Rotherham.
Wolves' route to victory became significantly easier after just 28 minutes when Nathan Doyle was given his marching order for a late challenge on McDonald that earned him his second yellow card.
Consequently, City boss Phil Parkinson opted to replace striker Aaron McLean with midfielder Chris Atkinson but, despite the numerical disadvantage - and the lack of a striker on the field - it was the Bantams who came closest to opening the scoring.
Three minutes into stoppage time the West Midlands outfit found the breakthrough through McDonald.
Dicko secured the points midway through the second half, bundling Bakary Sako's cross into the net for the second goal of the match.