The centre-back scrambled the ball into the bottom corner of the Southend net from close range following Andrew Davies pass into the box.
The win ended Southend’s hopes of returning to the top of the table but was just reward for a Bantams side who dominated for much of the match, with winger Kyel Reid proving a thorn in the Blues’ side.
City went closest early on with a Michael Flynn free-kick which was saved by Luke Daniels, while Southend did not test City keeper John McLaughlin in the first half.
The hosts improved after the break and the introduction of Lee Sawyer and Anthony Grant resulted in the latter having their first shot on target, an effort easily held by McLaughlin.
Liam Dickinson forced McLaughlin to parry his free-kick from the edge of the area – but Oliver then grabbed the winner and the Bantams held on for four minutes of stoppage time.