An early goal from Francois Zoko settled a poor-quality game played on an awful pitch.
Reds had some good spells with captain for the night Izale McLeod heading their best chance wide with seven minutes to go but things just wouldn't drop for the visitors in the City box.
Bradford City goalkeeper Jordan Pickford under pressure in the second half
Interim Manager Dean Saunders had made one change to the Reds’ line-up with Ryan Dickson, who had a slight stomach strain, on the bench as Darren Ward came into central defence and Sonny Bradley moved to left back.
The notoriously bad Valley Parade pitch was clearly going to be a factor. It was cut up badly after the warm-up and in the early stages both sides struggled to find any fluency.
But Reds fell behind in the softest possible manner on nine minutes.
Goalkeeper Lewis Price failed to claim a cross from the right and ZOKO outmuscled Lewis Young to send a looping header into an empty net.
Bradford, who had made seven changes with this Saturday's FA Cup quarter-final in mind, sensed vulnerability in the visitors’ ranks and for the next 20 minutes or so penned Crawley back, without forcing Price to make any saves of note.
Zoko and the equally powerful James Hanson were causing problems, particularly when they isolated Young on the right so Saunders responded and changed to a 3-5-2 on the half-hour and gradually Reds began to get a foothold in the contest with Young and Gwion Edwards operating as wing backs and Lee Fowler in a deep role in front of the back three.
Crawley started to compete on equal terms in midfield and Fowler thought he had equalised on 39 minutes when he bent a free kick from 22 yards over the wall only for Jordan Pickford to fling himself to his right to push the ball to safety.
Pickford then made a more routine stop from Edwards' cross after he made a great break into the box before the Welshman fired over after cutting in from the left as Reds ended the half well.
Rain greeted the players at the re-start making conditions worse and both teams struggled to get any sort of momentum for the first 15 minutes of the second half.
Andy Halliday made a purposeful break into the box for the hosts before lashing his shot over before Crawley began to make some headway and captain for the night McLeod forced James Meredith to clear his header off the line only to be penalised for a shove on Pickford.
Saunders made a double change with 20 minutes to go when Dickson and Morgan replaced Mathias Pogba and seconds later McLeod was inches away from equalising when his 20-yard drive was deflected past a helpless Pickford.
Crawley’s top scorer squandered an even better opportunity with seven minutes to go. Gavin Tomlin’s diagonal ball picked him out at the far post but with just Pickford to beat from close range he headed agonisingly wide on the stretch.
Reds pushed Bradley up front in the closing stages but Bradford held on for the three points.
It was a frustrating night for Reds who must re-group and go again on Saturday against Bristol City.