An Alan Smith goal after a moment of brilliance from Mark Viduka gave Leeds all three points as they produce a superb performance against Lazio in Rome.
In an open Champions League encounter, the visitors had the lion's share of the chances and thoroughly deserved the victory over the Italian champions.
Leeds looked anything but overawed in the opening minutes and took the game to their Serie A opponents.
The Yorkshire side had the earliest chance after eight minutes, when a Lee Bowyer cross bypassed Viduka, Smith and Jonathon Woodgate in the six-yard box.
Kicked off the line
For Lazio, former Crystal Palace star Attilio Lombardo looked dangerous on the right-hand side for Lazio and gave Dominic Matteo a torrid time.
However, it was the home team who had another escape, when Eirik Bakke had his header kicked off the line by Lombardo from a corner after 16 minutes.
Lazio continued to look dangerous on the break. But two set-pieces gave them their best early chances.
Hernan Crespo hit the side netting from a Lombardo corner after 18 minutes.
The cross-bar was then rattled by Giuseppe Pancaro from a yard out after he out-jumped Jason Wilcox on 21 minutes.
Most-wanted
A Giuseppe Favalli cross was met by Marcelo Salas, whose header was kicked off the line by Woodgate.
On the stroke of half-time, wonderful skill from Viduka inside the box saw his cross just elude Lee Bowyer.
All the England Under-21 international could do was knock the ball wide, diving at full stretch.
In the second half, Leeds' central defenders held Lazio at bay as Pavel Nedved began to show the form that has made him one of the most-wanted players in Europe.
Leeds' first attack of the new half was through the impressive Olivier Dacourt.
His snap-shot from 20 yards beat keeper Angelo Peruzzi but went inches over the bar on 58 minutes.
Dacourt dominant
Nedved's runs continued to test the away side and a shot in the 60th minute flew wide with Paul Robinson beaten.
Viduka was unlucky not to break the deadlock after 65 minutes when he connected with a Bowyer cross only for Peruzzi to tip over.
A minute later, Woodgate failed to capitalise on a chance when he scuffed wide from 15 yards out.
Frustration began to creep in for Lazio, who found Dacourt dominant in a defensive midfield role.
He used his aggression to dictate the play and stifle Lazio's intricate passing game.
Viduka for his part continued to press his markers, who doubled up on the striker to stifle his dribbling master-class.
Robinson was called into action in a one-on-one with Crespo after the Leeds defence was caught napping but he spread his body to block the attempted chip.
But then Leeds struck on 80 minutes and maintained their stranglehold on the game to wrap up a fine European night for the Elland Road club.
Lazio: Peruzzi, Favalli, Couto, Nesta, Pancaro, Nedved, Simeone, Veron, Lombardo, Salas, Crespo. Subs: Marchegiani, Negro, Mihajlovic, Pesaresi, Gottardi, Ravanelli, Colonnese.
Leeds: Robinson, Matteo, Woodgate, Radebe, Kelly, Wilcox, Bakke, Dacourt, Bowyer, Viduka, Smith. Subs: Milosevic, Harte, Kewell, Huckerby, Mills, Burns, Maybury.
Referee: C Colombo (France)