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.
1. Glenn Morris - 7
Pulled off an excellent diving save to preserve the Reds lead in the first half. Not much he could do about Bradford's goal Photo: Steve Robards
2. Archie Davies - 6
Decent game for the Reds. On hand to make some interceptions and link the wide men on the right Photo: Pete Norton/Getty Images
3. Tom Dallison - 7
Held the back line together superbly with the returning Francillette. Unruffled at the back Photo: Pete Norton/Getty Images
4. Ludwig Francillette - 9
Imposing at the back on his return from injury. Strong in the tackle, wasn't afraid to move play up the field and was a constant danger at set pieces. Voted man of the match by the match sponsors. Photo: Pete Norton/Getty Images