The Championship outfit held off a late fightback to secure passage into the fourth round against a lackluster Toffee side at Elland Road.
With just four minutes on the clock, White pounced on a loose ball some 35 yards out and set off on a mazy run. Showing terrific close control, he saw off Marouane Fellaini with ease before evading the tepid attempts by Sylvain Distin and curling a superb effort around Jan Mucha to put the home side 1-0 up.
Everton showed nerves against its lower-league opposition as the combination of White and Michael Brown in the center of midfield pulled the strings against David Moyes’ lackluster charges.
Luciano Becchio was giving Seamus Coleman a torrid time down the left flank - finding pockets of space with ease relative ease – however, at the other end of the pitch, Leeds’ weak link was Tom Lees, who seemed to struggle with the attentions of the spirited Victor Anichebe.
Everton could not seem to handle the added impetus the Championship side possessed, but the top-flight side was not helping itself with a number of below-par performances; most surprising was Fellaini’s inability to assert himself at all.
And, as the game entered stoppage time at the end of the first half, Becchio could have – and probably should have – extended Leeds’ lead after getting on the end of an El-Hadji Diouf corner to power a header straight at Mucha, with Steven Naismith hacking the rebound off the line.
Moyes rang the changes at halftime, bringing Steven Pienaar and Phil Neville on for underwhelming duo of Magaye Gueye and Junior, while pushing Fellaini farther forward.
The Belgium international immediately had more impact on the game, but Everton still struggled to impose itself.
With an hour played, the Premier Leaguers had still not registered a shot on target – and they could only blame themselves.
Anichebe, who could not be faulted for his lack of effort throughout the game, darted down the left flank before cutting inside and swinging an inch-perfect cross towards Steven Naismith in acres of space, only for the striker to flash the header wide.
And Everton were duly punished as, just minutes later, El-Hadji Diouf simply rolled a free kick from near the corner flag to the edge of the area for Danny Pugh to guide the ball towards goal and allow Austin to finish off the job from two yards.
However, with 10 minutes remaining, Steven Pienaar lofted in a free kick from 40 yards towards the the industrious Anichebe to flick on for Sylvain Distin. The center back’s header took a nick off Pugh and looped over Jamie Ashdown to give Everton a flickering hope of a comeback.
However, despite a long-overdue hassling of the Leeds defense, the Premier League side could not find the equalizer following a performance which lacked urgency and desire throughout.