The away side started with plenty of intent and had no trouble creating chances. Sebastian Bassong and Peter Crouch were the first to spurn opportunities.
Michael Doyle had the home side's first sniff of goal with 13 minutes on the clock, forcing Gomes to make a save.
As the first half developed it seemed as if Jermain Defoe and Casper Ankergren were having their own personal duel.
The Danish keeper first squared up to the England man in the 12th minute when he shot wide.
Then 10 minutes later Defoe was put clean through Jermaine Jenas. With just the keeper to beat he fired straight at Ankergren.
With half an hour on the clock the situation was repeated. This time Lubomir Michalik stopped Defoe in his tracks before he could get his shot away.
After 34 minutes Defoe tested Ankergren again, and then he finally got his goal.
David Bentley, taking advantage of a rare run in the Spurs side, beat Andy Hughes down the right wing and pulled the ball back for Defoe. With his back to goal the striker turned and hit a rather sliced shot that looped in under the bar.
Then on the stroke of half time Leeds levelled matters. Jermaine Beckford's shot was acrobatically blocked by Gomes and Luciano Becchio was on hand to tap in.
The second half followed a similar pattern to the first.
Defoe resumed his duel with Ankergren minutes after the restart, nearly beating the big Dane with a dipping shot.
Bentley was the fulcrum of the majority of his side's attacking verve, setting up chances for Defoe, Crouch and Kranjcar and also having a shot on goal himself.
Defoe thought he had given Tottenham the lead after 67 minutes but he was offside.
He didn't have to wait long to grab what proved to be the winning goal. To no great surpirse Bentley was the provider for his compatriot, who steered the cross into the net.
The bar denied Crouch a third, before Defoe sealed his hat trick.
He raced clear as Leeds searched for an equaliser, rounded Ankergren and prodded home.
The dream is over for Leeds United, but it has been an incredible journey.
(By Alan McGuinness, goal.com)