But Crawley were forced to hold off a late fightback from the non-league outfit.
Sergio Torres had an early effort palmed away before Josh Simpson broke the deadlock on 36 minutes, latching on to Michael Jones’ throughball and poking past keeper Jamie Butler.
The Blues did improve after the break with Howard Newton forcing a smart save from Paul Jones and Craig Brown dragging an effort wide.
Clarke then looked to have made Crawley’s progression into round two certain when he tapped home a second on 70 minutes.
Alan Tait’s goal eight minutes from time for the Blues worried Crawley but they clung on to avoid a replay despite late pressure, which saw Newton hit the post.