Even Hornets boss Ray Lewington admitted the 87th minute penalty should not have been awarded after City's Lewis Emanuel shoulder charged Jermaine Pennant off the ball to send him spinning.
Nottinghamshire referee Alan Butler pointed to the spot and after lengthy protests by City defenders, Cox stepped up to blast home for his sixth goal of the season.
While it was a cruel decision for City, the fact is Watford were denied two earlier penalty claims which looked far more valid than the one awarded to them.
Watford who have struggled recording only one victory in the previous seven outings totally dominated the first half. It was so one-sided it took the visitors 45 minutes to muster a shot.
Solid defending by Bradford along with poor decisions from Watford meant the visitors were still in the hunt at half time.
Substitute Dominic Foley broke through early in the second half, but elected to shoot for the near post enabling Aidan Davison to make a smart save down to his right.
City tested Watford keeper Alec Chamberlain when Claus Jorgensen turned to send a dipping shot goalwards and Chamberlain was forced to stretch to tip over.
City played a much tighter game in the second half and Watford found chances hard to create.
Sub Gifton Noel-Williams sent a couple of shots just wide on the turn and then when almost through was taken out by Jamie Lawrence, but the referee waved play on as he had in the first half when Simon Francis had handled a cross from Pennant.
Bradford had six players booked as they tried to frustrate Watford.