The Bantams cruised past their fourth-placed guests with goals from James Hanson, Nahki Wells and Craig Fagan to extend their unbeaten league run to five matches.
The Shrews grabbed a late consolation through Marvin Morgan, his ninth of the season, after Bradford had David Syers sent off for a professional foul, but the hosts were comfortable in victory.
Hanson handed the west Yorkshire outfit the lead after 24 minutes. The striker rose highest to nod Andrew Davies’ cross beyond Chris Neal in the Shrews’ goal to register his ninth goal of the campaign.
And the home side doubled their lead five minutes later when Bermudan international Wells buried the ball into the bottom right-hand corner of the net with a left-footed shot from the edge of the area.
Fagan’s 12-yard volley effectively killed the game off four minutes after half-time and, although Syers received his marching orders with 20 minutes remaining following a foul on Nicky Wroe, all Shrewsbury could muster with the man advantage was Morgan’s volleyed effort after 78 minutes.