Swindon moved four points clear of the drop zone as Anton Rodgers' 20th minute free-kick was the difference at The County Ground.
City were sluggish off the mark in the early stages and Swindon almost found the net through Nathan Delfouneso's curling shot but Colin Doyle was equal to it.
The hosts were well on top when they took the ascendency through Rodgers' sublime free-kick, which left Doyle with no chance as it hit the top corner.
Swindon had the ball in the net for a second time soon into the second half but Town skipper Jon Obika was adjudged offside.
The Bantams responded in the fashion expected by a team sat fourth in the table, with Haris Vuckic impressing in a cameo.
James Hanson also wasted two good opportunities to draw his side level, while Obika missed a chance to settle the game in the six additional minutes.
Despite falling to defeat, Bradford remain fourth in League One but now face a five-point gap to the automatic promotion places.