Teenage prodigy Wayne Rooney came off the bench to give Everton their first league win at Elland Road since September 1951.
Picking up the ball 30 yards from the Leeds goal he went past Eirik Bakke as though he was not there, powered his way to the edge of the box and drilled a shot low into the corner of Paul Robinson's net.
Two sides attempting to claw their way out of mid-table largely cancelled each other out for much of the first half, although Everton created the better chances.
A series of wickedly inswinging corners from Mark Pembridge troubled Leeds at the near post while Robinson had to be alert to keep his goal defended.
He turned a Pembridge free kick away as it dipped just under his bar, parried a fierce drive from Tomasz Radzinski, and smothered a shot from Lee Carsley when Leeds left the midfielder completely unmarked inside the box.
Leeds struggled to create many clear-cut opportunities although Harry Kewell went close with a dipping 20-yard shot that flew just over the bar.
Alan Smith had a penalty appeal turned down when he felt he was held, and Nicky Barmby was sent tumbling by Richard Wright but referee Neale Barry waved away Leeds appeals and booked Barmby for diving.
Both sides were more enterprising after the break with Leeds signalling their intention in the first minute when Smith and Mark Viduka set up Barmby but the diminutive midfielder was denied by a brave save from Wright.
From the resulting corner, Bakke's diving header flew just wide. At the other end Radzinski's pace twice got him in the clear but again he was thwarted by Robinson, who looks more impressive the longer the season goes on.
As Leeds stepped up the pace Kewell had a shot deflected inches wide and Jonathan Woodgate's header from the corner was cleared off the line by Tony Hibbert.
With the game apparently heading for a draw, enter Rooney and within five minutes the fairy tale continued