Until his 91st minute strike a superb display of goalkeeping by Paul Henderson, allied with some poor finishing, looked to have denied Blackpool victory.
Despite freezing conditions and an uneven pitch both sides served up some attractive football. City had two early chances blocked and Nicky Summerbee should have done better than blast two shots wide.
The Seasiders came back strongly and good work from Danny Coid almost forced David Wetherall into conceding an own goal, but Henderson produced the first of his series of fine saves to keep the defender's sliced clearance out.
Blackpool finally turned their pressure into a goal in the 48th minute when Martin Bullock crossed to the far post for Keith Southern to head home with the help of a deflection.
In the 54th minute a terrible mix up in the home defence handed City an equaliser. Defender Tony Butler, making his home debut, mistimed his back pass and Andy Cooke intercepted to score from an acute angle past Lee Jones.
From then on Blackpool laid siege to Henderson's goal, hitting the woodwork twice and forcing the City keeper into a series of great stops.
At the other end Bradford still had chances and Dean Windass should have scored with a header, but somehow he contrived to bullet it over the bar.
In the three minutes of added time the home side finally found a winner when Parker cut in from the right to score with a low drive.