The Gills were second best in a first half of few opportunities at Valley Parade.
With their Capital One Cup Final against Swansea a fortnight away, Bradford were chasing the confidence boost of a first league win since Boxing Day in their last home game before Wembley - and they created the better openings.
James Hanson headed inches over the bar from Kyel Reid's cross and it needed a superb double save from Stuart Nelson to foil Bradford captain Gary Jones and top scorer Nahki Wells.
Bradford keeper Matt Duke didn't have a shot to save until Chris Whelpdale tested him with a low drive after 52 minutes but the Bantams were caught out 12 minutes later. Vastly experienced Deon Burton lobbed the ball over the defence and Cody McDonald fired past the stranded Duke.
Bradford's applied late pressure but could not conjure an equaliser.