Southampton loanee Will Ferry put the Reds ahead on 39 minutes. The midfielder volleyed home from Jake Hessenthaler's cross to bag his first goal for the club.
Nick Tsaroulla's screamer, after a buccaneering run into the area, doubled the Crawley advantage on 73 minutes.
Callum Cooke put Crawley hearts in mouths with a goal for Bradford with nine minutes remaining.
But the Reds held on to extend their home run, and move up to eighth in League Two. Here's how we rated John Yems' men.
5. Nick Tsaroulla - 8
Assured performance at left back in the first half. Bombed forward to rifle home the Reds' second
Photo: Simon Dack/Telephoto Images
6. Will Ferry - 8
Was at the heart of everything good for Crawley in the first half. A constant thorn in the side of the Bantams defence and put the Reds ahead on 39 minutes. Replaced by Kwesi Appiah in the second half due to an injury
Photo: Steve Robards
7. Jake Hessenthaler - 7
Headed just over from a tight angle before sending in an excellent ball for Ferry to score. Another solid display from the midfielder
Photo: Pete Norton/Getty Images
8. Jack Payne - 7
Another tidy game in the centre of the park for Payne. Forming an excellent partnership with Hessenthaler
Photo: Jamie Evans/UK Sports Images Ltd