Richard Cresswell scored two goals and David Healy one as second placed Stoke were seen off with two goals in a minute.
Davies chances to become full-time manager of Preston must be very good, but away from home could be the key.
Stoke had a volley by Marcus Hall from a cross from the right by Darel Russell which went over the bar after 14 minutes.
Preston's Dickson Etuhu had a shot which was blocked by Gerry Taggart and Halls from the edge of the box.
Simon Lynch crossed the ball to Cresswell but as he pounced the ball was cleared by John Halls.
Preston made it 1-0 after 27 minutes when a right-wing right-foot cross by Graham Alexander fell to Cresswell, who turned and shot right-footed into the bottom left-hand corner from ten yards.
Healy took a quick free-kick from 40 yards after half an hour and Stoke City keeper Ed de Goey tipped the ball round the post for a right-wing corner.
Ade Akinbiyi was booked for dissent, before he had a header from a David Brammer cross which went wide of the left-hand post.
Halls shot wide of the right-hand post after 51 minutes and Clive Clarke had a 15-yard left-foot shot saved by Andy Lonergan.
Simon Lynch had a shot saved from 12 yards after an hour and then had a 15-yard header tipped over the bar by the keeper for a right-wing corner.
Lonergan saved again from a long-range Russell shot and Preston made it 2-0, when a Paul McKenna left-wing cross fell to Cresswell and his 15-yard right-foot shot went into the bottom right corner after 79 minutes.
Preston made it 3-0 a minute later when McKenna again fed the ball through for Healy whose shot went into the top right corner of the net.