The Bolton striker, a last-minute loan signing for North End on transfer deadline day, produced a superb display on his debut to keep Simon Grayson’s side in the play-off pack.
Davies opened his account in the 65th minute when he did brilliantly to find space on the edge of the box to fire into the top corner.
The hosts’ lead was doubled just six minutes later when Jack Grealish hauled Davies down inside the box, despite Notts claiming the tackle had been just outside the penalty area.
But Joe Garner took responsibility for the spot-kick and buried it firmly past County goalkeeper Kevin Pilkington.
Notts kept plugging away, but their best chances came in the first half when Enoch Showunmi headed over the crossbar, while Grealish fired wide.
But they were also indebted to Pilkington, who made a series of stunning saves to keep the score down – denying Paul Gallagher and Garner with fine saves.