The Premier League side have lost just once in their last nine games to pull clear of the relegation zone.
But they were headed for defeat at half-time to second-tier Derby after Chilean international Ben Brereton Diaz drilled a strike into the bottom corner.
Joel Piroe had seen a penalty saved by Jacob Zetterstrom before Leeds fell behind but the Dutch striker redeemed himself by playing a part in the comeback.
Jaka Bijol played the ball into the area and Piroe's neat step-over allowed Willy Gnonto to smash home a 55th-minute equaliser.
Just four minutes later Piroe's low shot was parried by Zetterstrom and Ao Tanaka slotted in the rebound. The visitors made sure of victory in stoppage time when James Justin rounded off a slick counter-attack.