It had started well for Bradford, who denied their hosts a sixth straight clean sheet with a deserved goal inside a quarter of an hour.
A ball over the top allowed Andy Cook to set up strike partner Clayton Donaldson who smashed in his seventh of the season from close range.
But the visitors’ lead was short-lived as Vale hit back straight away. Luke Joyce’s ball in fell to Theo Robinson, who had time to compose himself and fire home the equaliser.
The Valiants went ahead after 32 minutes when Nathan Smith was sent flying by Oliver Crankshaw as he chased a through-ball, referee Ben Speedie pointing to the spot without hesitation.
Conlon slotted in the penalty to send the hosts in a goal to the good at half-time.
With chances few and far between in an evenly-matched second half, the closest Bradford came to a goal was a low drive by Cook which goalkeeper Scott Brown getting down well to save.
That effort aside, Vale comfortably made it nine games unbeaten while Bradford suffered their fourth straight loss.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you’ll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click HERE to subscribe.