Neil Warnock was forced into making a number of enforced changes due to injury with Paddy Kenny, Lee Peltier, and Adam Drury all missing out on the starting line up due to injury.
Aidy White was one of those players recalled to the starting line-up and he fired Leeds ahead inside four minutes. The youngster showed great skill to beat two men in the middle of the park and was allowed to advance before drilling the ball home for a stunning individual strike.
It was a wonderful effort, coming after Rodolph Austin won the ball, and was a great start for Leeds against the Merseysiders.
United played some good stuff early on and looked to pressure the Premier League side. Everton were clearly unsettled after the goal and were on the back foot.
The pressure won United a free-kick on the edge of the box shortly before the half-hour, and Michael Tonge sent the shot just wide of the upright.
As the game headed towards half-time, United threatened to open up Everton again, and White forced another save out of visiting goalkeeper Jan Mucha. There was also an injury stoppage before the break when Jason Pearce needed bandaging up after a head collision.
In first half stoppage time, Luciano Becchio thought he had scored with a header, but the ball was cleared off the line.
United were good value for the lead, and started the second half on the front foot, El-Hadji Diouf drilling in a low early cross. Sam Byram also sent a shot just wide after more good work.
But Everton did create a good chance shortly before the hour when Victor Anichebe did well out wide to pick out Steven Naismith, but his far post header was wide. Anichebe also sent a shot fizzing across the goal-line.
When United came forward again, Austin won a free-kick on the edge of the box. When the set-piece was taken, Danny Pugh drilled it into the box, and Austin got the decisive touch to turn the ball home.
Everton's response came when a long range shot from Marouane Fellaini called Jamie Ashdown into action for the first time, and the United keeper made a great block.
But still United continued to press and Byram won a corner after more good work in the box.
The visitors did throw themselves a lifeline with 10 minutes remaining, though, when Sylvain Distin looped a header over Ashdown from a free-kick into the box.David Moyes' men pushed forward desperately and were unlucky not to get a spot-kick when Victor Anichebe was bundled over by Jason Pearce, but Leeds deservedly clung on.