Max Gradel's 17th goal of the season put Leeds in front but their lead was short-lived as Derby produced a spirited fightback with two goals in as many minutes.
Jamie Ward equalised from close range and Davies picked the perfect time to score his first goal for the Rams as he powered home an unstoppable volley to consign Simon Grayson's side to a third consecutive away defeat which leaves them just a point above seventh-placed Nottingham Forest.
Both sides struggled to get into their stride in a cagey first half but Leeds looked more dangerous going forward.
Rams midfielder Ben Davies breathed a sigh of relief after 23 minutes when he lost the ball deep in Leeds' half and the visitors broke quickly but Barry Bannan was off target with his left-foot finish.
Derby were almost caught out again five minutes later when Luciano Becchio chested the ball into the path of Jonny Howson and the Leeds skipper burst forward before unleashing a right-foot drive which was parried away by goalkeeper Brad Jones.
The home side looked devoid of ideas going forward but when Robbie Savage whipped in an inviting crossed from the right Steven Davies was agonisingly close to connecting and Leeds keeper Kasper Schmeichel was alert to the danger and smothered the ball with Ward lurking behind him.
Ward should have put Derby in front within a minute of the restart after he was sent clear by Stephen Pearson but the on-loan striker showed a lack of composure and fired tamely wide of Schmeichel's near post.
Derby had more of a spring in their step and looked far more lively going forward.
Ben Davies skipped away down the right and flashed the ball across the face of goal but Steven Davies and Ward were unable to apply the finish.
But it was Leeds who were in front 12 minutes into the second half when Gradel gave Jones no chance with a vicious right-foot drive from just outside the penalty area.
Derby were in no mood to feel sorry themselves though, and they were level three minutes when Pearson skipped past former Rams defender Paul Connolly and crossed for Ward, who was on hand to finish at the far post.
And two minutes later Leeds were stunned when Derby took the lead courtesy of a sweetly-hit strike from Ben Davies.
Pearson was once again the provider, this time with a pinpoint corner from the left which the former Notts County midfielder met with a sublime right-foot volley from the edge of the that flashed past the helpless Schmeichel.
Ward fired wide of the near post and Steven Davies had a free-kick tipped over by Schmeichel.
Leeds threw men forward in the closing stages but Derby stood firm for three precious points.