With central defenders Lincoln Adams and Mark Gray
both suspended, manager Peter Rinkcavage was forced to reshuffle and it was a couple of misunderstandings by the cover which gave the visitors their goals.
Danny Walsh picked out Ollie Ryan in the 11th minute, only for his shot to be blocked at point blank range by John Lamb, with Bradford responding, Jordan Deacey testing Stephen Dickinson with a low 20 yard drive two minutes later.
A strong shot from Brad Grayson was only parried by Lamb after 23 minutes, but Stuart Ludlam
lifted the rebound over, while a free-kick from James Ashmore in the 34th minute was only half cleared and Ben Turner screwed his effort wide.
A misplaced clearance by David Cyrus dropped straight to Rob O'Brien in the 45th minute, and he rifled the ball in from 22 yards to give Park Avenue the lead.
Seven minutes after the interval, Cyrus sold Dickinson short with a back pass which was intercepted by Matty James whose first time lob went across the face of goal, O'Brien chasing the ball and collecting it on the left before cutting inside and finding the net from an acute angle.
Ollie Ryan beat two men in the 59th minute before finding James Ashmore who shaved the bar with a 25 yard drive, and the Blues forced four corners in quick succession, ending with Alex Callery
striking a low 20 yard drive which Lamb held at the second attempt.
There was a let off for Frickley in the 73rd minute when James had a shot parried by Dickinson before slicing the rebound wide.
Danny South, who had replaced Grayson, tested Lamb with a header in the 80th minute before reducing the arrears seven minutes later, outjumping the visiting defence to head in a pinpoint cross from the left by Ryan Mallon.
Bradford were rocking, and Ashmore beat Lamb with a storming 25 yard free-kick in the fourth minute of stoppage time, only for the ball to come back off the bar.
Frickley: Stephen Dickinson, Kelvin Bleur, Ben Turner, Danny Walsh, David Cyrus, Stuart Ludlam
, Ryan Mallon, James Ashmore, Brad Grayson (Danny South 67min), Ollie Ryan, Mark Whitehouse
63min); unused subs, Grant Darley, Ben Saynor
Bradford: John Lamb, Adam Clayton, Nicky Boshell, Jordan Deacey, Nathan Hotte, James Riley, Michael Duckworth (Dempsey Smith 63min), Ross Daly, Matty James (Martin Drury 85min), Rob O'Brien, Aiden Savory (Curtis Bernard 63min); unused subs, Billy Law, Richard Marshall.
Referee: Mr Wayne Grunnhill