Three goals from Rob Hulse in a 12-minute spell just before half-time drove away Leeds' hangover after their weekend defeat by Ipswich.
But Derby must have felt as mugged as Leeds did by the Tractor Boys, because they too had plenty of chances in an entertaining game in which both defences struggled to contain rampant forwards.
The Rams saw Morten Bisgaard send a dipping 24-yard free-kick inches wide of the post and minutes later Paul Peschisolido was through with only Neil Sullivan to beat, but the Leeds keeper stood up and pulled off the first of a series of great saves.
Most of United's efforts had been much weaker up until then but in the 32nd minute Robbie Blake, on for the injured Richard Cresswell, had a shot parried by Lee Camp and when the ball was put back into the area, Hulse scored from close range.
His second came five minutes later when Eddie Lewis sent in a high cross and Hulse managed to climb above Camp and deflect it in.
And he rounded off a stunning spell from Leeds a minute before the break when Lewis cut inside his marker and shot low. Once again Camp could only parry the shot and Hulse hit home the rebound on the turn.
It was harsh on a Derby side containing Seth Johnson, back at Elland Road for the first time since being released by Leeds in the summer.
The Rams had looked very bright with Tommy Smith, Peschisolido and Stern John causing plenty of problems.
Visiting boss Phil Brown made three substitutions five minutes into the second half and Derby again stretched the Leeds defence, but struggled to make the breakthrough.
When it came it was from an in-swinging Bisgaard corner that appeared to be helped in by Sean Gregan.
However, it was scant reward for a performance that deserved more.