United were languishing in the Championship with off-field ownership problems weighing heavily on the LS11 club to hamper on-pitch progress.
The Toffees, meanwhile, were enjoying Premier League football on a regular basis and challenging for Europe under then head coach David Moyes.
A meeting for a spot in the last 16 of the Capital One Cup threw the two teams together and it was the second division hosts who came out on top on a wet and windy September night in West Yorkshire.
A little over 21,000 had made the trip to the Whites home ground and it took just four minutes for Leeds academy product Aidy White to get the majority of those off their seats.
White charged from midfield and jinked inside and out of the visiting defence before curling a shot into the top corner of the net to spark wild celebrations.
Rodolph Austin then doubled the lead for Neil Warnock's side in the second half as the Jamaica international guided a Michael Tongue shot home.
French defender Sylvain Distin did reduce the deficit late on for Everton thanks to a for the Merseyside club but it was Leeds who held on for victory on a night of rare success under the lights.
7. Leeds 2 Everton 1
Leeds United fans watch on in the stands at Elland Road. Photo: Varley Picture Agency
9. Leeds 2 Everton 1
Rodolph Austin fires a shot at goal as Leeds United look to score again.
10. Leeds 2 Everton 1
Michael Tongue's shot is guided into the bottom corner by Rodolph Austin.
11. Leeds 2 Everton 1
Leeds United's players celebrate after doubling the lead in LS11 through Rodolph Austin. Photo: Varley Picture Agency
12. Leeds 2 Everton 1
Whites head coach Neil Warnock salutes the crowd post-match. Photo: Getty