The Bantams had been outclassed in the first half but responded admirably after the break to take the lead when loanee Dickson finished with aplomb after racing clear.
With Fleetwood struggling for inspiration, the points looked to be heading back to Bradford only for Parkin to come off the bench and ensure honours ended even with a 75th minute penalty.
After levelling the in the final minute of the first half through an exquisite free-kick by Nahki Wells, City were clearly fired up on the restart as they put in a vastly improved shift.
Ryan Dickson ensured there was reward for the visitors’ enterprise on 52 minutes when he finished coolly after being released by a fine ball from Carl McHugh.
The Bantams then had a very good shout for a penalty turned down when Shaun Beeley, who had been at fault for Dickson’s goal, bundled Wells to the floor
Referee Tim Robinson, however, waved away the appeals and Bradford’s sense of injustice was only added to 15 minutes from time when the official pointed to the spot after the ball had struck James Hanson on the hand.
Jon Parkin did the rest from the spot, albeit only after his former team-mate Matt Duke had, at first, kept out the effort to ensure it was a point apiece from an entertaining contest