The Seagulls' hotshot bagged the winner after 28 minutes but his third goal in three games could not have been more debatable.
Brighton, looking for the win which would lift them off the bottom, were always dangerous on the break and when Zamora's strike partner Gary Hart floated over a cross from the right the alarm bells were ringing.
Zamora powered a downward header towards goal at the far post and although Bantams keeper Aidan Davison looked to have clawed the ball away the referee awarded the goal after getting the nod from his assistant.
It was just the sort of break a relegation-threatened side rarely gets and after last week's win over Wolves it was a real tonic for the Seagulls.
Bradford, who had only lost once in their last six League games, struggled to find their form and with Zamora a constant threat the visitors fully deserved an unlikely double over the Bantams.
It could have all been so different if Brighton keeper Ben Roberts had not produced a stunning ninth minute save to block a close-range header from Bradford skipper Ashley Ward.
It was one of Bradford's few clear-cut chances and even goal machine Claus Jorgensen could not drag them back.
The Dane was hunting a club-record equalling tally of seven goals in as many matches but like his team-mates, he was firing blanks.
City came closest to levelling in the 70th minute when teenage midfielder Simon Francis rattled the Brighton bar with an angled shot.
Davison kept his side in an increasingly niggly contest with superb saves to deny Hart and Zamora but there was more controversy in a frantic finale.
Keeper Roberts lost his bearings when he rushed out to claim a high ball but Mr Salisbury waved away Bradford's appeals as they protested that he handled outside the box.