The visitors deservedly took the lead after 34 minutes when a curling cross from the left by Will Hayhurst was turned into his own net by County youngster Haydn Hollis.
Notts were unlucky not to level with what was their first attempt on goal after 43 minutes when substitute Curtis Thompson was denied by goalkeeper Declan Rudd after being put through by Neal Bishop. Jeff Hughes followed up with a clever lob which landed on top of the crossbar.
Preston's Stuart Beavon then found himself clean through on goal as Grayson's side broke away seconds before half-time but his strike was blocked by County keeper Bartosz Bialkowski.
Substitute Yoann Arquin should have equalised in the 61st minute but he was thwarted by a fine save by Rudd before North End skipper John Welsh missed a chance to seal all three points as he finished tamely when through after 84 minutes but one goal proved enough.