Felipe Morais tried to give the hosts the lead inside the opening minute with a volley from 20 yards out, but his shot finished well high of the bar.
Morais threatened from a corner, curling the ball in dangerously, but Brian Jensen came off his line to make sure Bradford did not get the shot away.
However, it was the visitors that broke the deadlock just a couple of minutes later when Oyebanjo slipped while attempting a clearance, allowing James Hanson to pounce on the loose ball and smash it into the back of the net.
Bradford upped their game again in a bid to restore their lead, and they did so just after the hour mark when Knott hit the ball in the volley from the edge of the box, with his finish going in off the post.
Mason Bennett made it three for the visitors when he timed a run from midfield to beat the offside trap and chip the ball over Jensen.
Mark Yeates had a chance to add another for Bradford inside the final 10 minutes after making a quick run down the wing, but he sent his finish high.
The result leaves Bradford second in the table, while Crawley sit seventh.