City dominated, having 16 shots to the hosts’ two, but could not take all three points.
Jamie Proctor headed home from Tony McMahon’s cross on 71 minutes to put Bradford in front.
But the Shrews grabbed an 85th minute equaliser when Jean-Louis Akpa-Akpro headed in Mat Sadler’s cross.
The draw leaves Bradford six points off the top two - with four games remaining - and five points ahead of Barnsley, who drew 0-0 at Burton.
Boss Phil Parkinson said: “We dominated the game, played really well and created numerous chances. I couldn’t have asked for much more in terms of the way we played.
“We’ve had a disallowed goal, which I don’t think should have been, and our customary two penalty appeals again, the keeper’s made numerous saves and we’ve had 17 corners.”
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