Bobby Zamora scored after 21 seconds to build on Fulham's first-leg lead and send the London club through 3-1 on aggregate. It's the deepest Fulham has gone in European competition.
“It's nice to make history and I'm so delighted for the players,” Fulham manager Roy Hodgson said. “They were gutted by the goal we conceded in the last minute of the first leg at Craven Cottage and it's fantastic they've come here and kept a clean sheet.” If Fulham is to reach the final at Hamburg's stadium it must now eliminate the German club, which made the semifinals by beating Standard Liege 5-2 over two legs.
Liverpool will play Atletico Madrid in the other semifinal after overturning a 2-1 first-leg deficit against Benfica to advance 5-3 on aggregate.
Atletico went through thanks to the away-goals rule, a 2-2 draw at Valencia last Thursday being followed by a 0-0 home draw in the second leg. The semifinal first legs are on April 22, with the return fixtures the following Thursday.
The victories for Fulham and Liverpool ensure the world's wealthiest domestic league will continue to have representatives in Europe this season. England's last Champions League hopefuls, Manchester United and Arsenal, were knocked out in this week's quarterfinals.
“It's very good for England,” Liverpool manager Rafa Benitez said. “Hopefully we will see Fulham in the final and we can talk about two English teams there.” Fulham, which ousted UEFA Cup holder Shakhtar Donetsk and Juventus in the previous rounds, couldn't have hoped for a better start in Germany. Zamora picked up a short pass from Zoltan Gera, turned past Jan Simunek and slotted his finish inside the right-hand post to net his 19th goal of the season.
Fulham then withstood Wolfsburg pressure to progress with some comfort.
At Anfield, Liverpool was facing a Benfica side on a 27-match unbeaten run but Dirk Kuyt headed the host in front in the 28th minute, latching onto Steven Gerrard's corner to make it 2-2 on aggregate.
The goal was initially ruled out as the referee's assistant on the right flank flagged for offside. But after Fernando Torres led Liverpool's protests, referee Bjorn Kuipers reversed the decision and Kuyt was able to end a 1,084-minute goal drought.
Six minutes later, Lucas Leiva gave Liverpool a two-goal cushion after completing a swift counterattack.
Having being released by Yossi Benayoun, Gerrard sent a defense-splitting pass through to the advancing Lucas, who rounded goalkeeper Julio Cesar and slotted into the net.
Another lightning-quick break forward saw Liverpool go 4-2 in front on aggregate in the 59th minute. After successfully defending a Benfica free kick, Javier Mascherano dispatched the ball to Benayoun, who raced down the left flank before passing to Kuyt on the right.
Kuyt crossed to Torres, who fired the ball into the net from six meters (yards).
Liverpool looked to be cruising into the last four, but Oscar Cardoza poked a low free kick through the defensive wall to make it 4-3 on aggregate with 20 minutes to go.
Torres netted again in the 82nd by clipping the ball over Jose Moreira, who had just replaced the injured Julio Cesar in goal.
Torres will now face Atletico, which he left in 2007.
Atletico withstood late chances and a penalty appeal by Valencia to draw 0-0 and advance on the away-goals rule.
Valencia had a penalty claim turned away in the 85th when Nicola Zigic appeared to be hauled down inside the area.
Atletico will be without striker Sergio Aguero for the first leg against Liverpool after the striker picked up a pointless yellow card for time wasting as he was substituted in the fourth minute of stoppage time.
“Liverpool's a great team and with Fernando coming here, we'll have to play a great game,” goalkeeper David De Gea said.
Hamburg arrived in Liege leading 2-1 from the first leg.
Mladen Petric scored twice in the first half - either side of Igor De Camargo's goal for Standard - to put the German club in further control of the quarterfinal.
Hamburg's Paolo Guerrero scored the third deep into second-half injury time.
