Bobby Zamora's fantastic scoring form in the competition continued as he handed the Cottagers a dream start in Germany with his sixth goal in his last seven games on the continent.
As Zoltan Gera fed the ball into his feet, he turned beautifully before sliding a left-footed effort beyond Diego Benaglio in the Wolfsburg goal inside 30 seconds at the start of the contest and it was mirror image of his goal in the first leg last week.
Fulham probed and pushed further forward in the opening exchanges and, with Damien Duff, Gera and Danny Murphy combining across the fringes of the final third, they continued to impress.
At the other end, Grafite had a goal correctly disallowed as he stabbed home following a fine stop from Mark Schwarzer on 12 minutes as the Wolves threatened.
Roy Hodgson's men refused to take their foot off the accelerator and they came close to grabbing a crucial second away goal when Gera's header was tipped wide by Benaglio.
As the first-half progressed, the hosts gradually clawed their way back into the game without creating any clear-cut chances.
Edin Dzeko was fortunate to stay on the pitch as he kicked the ball in the direction of the assistant referee as he flagged his push on defender Brede Hangeland.
Soon after Wolfsburg coach Lorenz-Gunther Kostner replaced defender Peter Pekarik with striker
Ashkan Dejagah as they frantically sought a way back into the game.
A little less than two minutes into the second-half, Chris Baird picked up a caution for time wasting at a throw in as the referee made his way into the clash.
Wolfsburg continued to battle but, as their men poured forward, Fulham looked more than capable of adding to their comfortable lead.
Zamora found himself one-on-one with Benaglio but his heavy touch allowed the stopper to make the save.
The England World Cup hope then turned provider as his magnificent clipped pass found Simon Davies in acres of space in the penalty area but the Welshman's downward strike was turned over by the busy keeper.
Murphy was the next to spurn a golden opportunity as Andrea Barzagli cleared off the line before Wolfsburg had their big chance to get back into the game.
Dzeko's broke free and his effort struck a post before falling kindly to Grafite but his effort was cleared off the line by Hangeland, who marshalled the back-four superbly throughout the evening.
With time running out, Fulham maintained their thrusting forward drives as they secured another majestic European win, securing a deserved victory over their illustrious German opponents.
They will now face another German outfit in Hamburg in the semi-finals after Bruno Labbadia's side saw off Standard Liege 3-1 in Belgium to record a 5-2 aggregate win.