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.
Callum Cooke put Crawley hearts in mouths with a goal for Bradford with nine minutes remaining.