It was so easy for North End, who dominated from the start and added two second-half goals to the one they picked up in the opening period.
Walsall, who suffered their first defeat of the season, were being outfought all over the pitch and Lee Holmes should have scored when he beat the offside trap on 19 minutes but he delayed his shot and James Chambers got back to deflect his effort for a corner.
Preston did take the lead in the 30th minute after a foul by Malvind Benning.
Joel Byrom took the free-kick from just outside a corner of the penalty box and his effort sailed just inside the far post.
It was the same story after the break and in the 58th minute Chris Humphrey strolled through to drive in a second for Preston, while three minutes later a howler by Benning let in Holmes to poke in number three.