Jones drove Crawley ahead after only six minutes with a bouncing right-foot shot from 25 yards into the bottom corner.
Skipper Josh Simpson shot over from the edge of the area and keeper Thorsten Stuckmann denied Paul Hayes as the hosts dominated.
Stuckmann then did superbly to tip over a goalbound header from striker Billy Clarke after Hayes' neat assist.
Preston's first attempt on goal did not arrive until the 33rd minute when captain John Welsh put a 30-yard free-kick wide.
Crawley ended the half totally on top and Clarke's cleverly-played free-kick was saved by Stuckmann.
Home keeper Paul Jones denied Jack King in a one-on-one situation shortly after the break and on-loan striker Hayes was similarly thwarted at the other end by Stuckmann.
Preston, who improved after introducing three substitutes in the second half, came close to snatching a point 20 minutes from time when King headed a Lee Holmes cross against the crossbar.