Derby County 2 The Whites 0
It was a deserved victory but the Rams had to work hard for their first home league win since December.
Michaek Ricketts, playing ahead of Brian Deane who was left on the bench, picked up a booking inside the first minute after colliding with Rams keeper Lee Camp.
Sean Gregan was also cautioned during the early stages for a heavy tackle on Morten Bisgaard, followed by the home side's Inigo Idiakez after a tussle with Gregan.
A defensive mistake by Pablo Mills then gave David Healy a chance but he failed to test Camp.
Idiakez fired a 25-yard free-kick which Neil Sullivan saved at the second attempt.
Sullivan then saved one-handed from Ian Taylor from a corner in the 15th minute.
Sullivan once again came to Leeds' rescue when he denied Smith's curling shot. The former Chelsea keeper was playing with a finger injury sustained in training, but he put on a show that must have impressed the new watching Scotland manager Walter Smith.
Grzegorz Rasiak headed wide from another corner and then, from a Frazer Richardson error, Marco Reich headed over a cross from the Polish striker.
George Burley's team dominated the first half without creating a clear opening.
The visitors had their moment at the start of the second half and almost went in front when Derby substitute Michael Johnson came close to slicing a clearance into his own net.
Danny Pugh was the next player to be shown a yellow card.
But the home side finally made their superiority tell, and it needed a well-worked goal from Smith to break Leeds' resistance, when he played the ball out to Jeff Kenna on the right and his first-time pass found Smith, who showed good control and composure to go past Sullivan and score from a tight angle.
Smith had been a threat to Leeds in the first half when his tireless running threatened to open up the visitors defence.
Derby looked uncertain in the early stages of the second half and when Mills gave the ball away, David Healy almost scored with a shot that Camp saved with his legs.
Then Reich sliced his shot wide but the goal gave Derby a cushion and they extended their lead in the final minute with Leeds pressing for an equaliser.
Derby broke out with Idiakez playing the ball through to substitute Bolder, whose shot from 18-yards deflected of the unlucky Richardson to leave Sullivan stranded.
The victory lifts Derby into the play-offs places for the first time in two seasons but it could have come at a cost.
Left-back Richard Jackson was taken off after 17 minutes and could now miss Saturday's FA Cup fourth round tie against Fulham.