The Rothosen opened the score before the break, but the Cottagers fought back in the second half and won 2-1.
Fulham recorded a 2-1 home win against Hamburg to book their ticket for the Europa League final.
Hamburg started the match with attacking intentions and immediately charged forward. Ruud van Nistelrooy opted to try his luck after only thirty seconds, but the Dutchmans shot was blocked and the chance went begging.
The hosts broke through the HSV defense only two minutes later. Bobby Zamora went for the one-two with Zoltan Gera and got the space to aim a shot at the Hamburg goal. However, the towering striker was denied by a superb save from Frank Rost to keep the score level.
The Germans opened the score halfway the first half. The referee awarded HSV a free-kick after Danny Murphy tripped Ze Roberto and Mladen Petric beat the Fulham goalie with a brilliant strike from 30 yards out.
Fulham won a free-kick 30 yards from goal and Simon Davies tried his luck. However, the Welshman couldn't quite match the heroics of Hamburg's Croatian, and blazed his effort well over the bar.
Jonathan Pitroipa caused the English defense all kinds of trouble and HSV's danger man cut inside from the right after 39 minutes of play before unleashing a fierce drive which fizzed just wide of Schwarzer's near post.
Fulham got their first chance of the second half at the hour mark. A corner kick from the left reached Damien Duff inside the area, but the former Chelsea winger aimed just wide at the far post.
HSV almost doubled their lead halfway the second half. Petric set up David Jarilim with an intelligent pass and the Czech Republic midfielder fired in a strong shot from a narrow angle. However, Schwarzer tapped the ball over for a corner kick.
The Cottagers restored parity after 70 minutes of play. Danny Murphy got all the time and space he needed to set up Davies with a good pass and the Welsh midfielder calmly finished after a brilliant individual move to make it 1-1.
Zoltan Gera became his side's hero in the 76th minute. The HSV defence failed to clear a corner kick from the right and the Hungarian midfielder didn't hesitate to fire the ball home from close range to shoot Fulham into the final.
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