Fulham must now overcome another German side to reach the final after Hamburg beat Standard Liege in the same half of the draw.
Breakthrough
Hodgson had stressed the need to pressure Wolfsburg early on and his side duly obliged by taking the lead almost immediately.
Gera laid the ball off to Zamora, who performed a clever turn to shrug off Jan Simunek on the edge of the box and beat Diego Benaglio with a calm finish.
The early goal seemed to settle any nerves and Fulham could have had a second six minutes later but Gera was denied by a fantastic save from Benaglio.
A rare error from captain Danny Murphy allowed Christian Gentner in at the other end but his shot was tipped around the post by Mark Schwarzer.
Wolfsburg struggled to get a grip on proceedings in an up-tempo game but thought they had equalised in the 12th minute before Grafite's effort was ruled out for offside from Andrea Barzagli's cross.
Gentner's inswinging corner then left Schwarzer flapping but otherwise Fulham looked in control of the tie, with Murphy and Dickson Etuhu firmly winning the battle in midfield.
Zamora's strike meant the Germans would have to score twice to force extra time and the home crowd began to vent their frustration at a lack of creativity.
Highly-rated Bosnia striker Edin Dzeko, who has been linked with a move to Chelsea, reminded Fulham of the threat he posed by flicking on a dangerous Zvjezdan Misimovic corner across the box in the 29th minute.
Dzeko found himself in the book soon after for kicking the ball away after referee Viktor Kassai had blown up for a petulant push on Hangeland.
Dangerous
Wolfsburg manager Lorenz Gunther Kostner replaced defender Peter Pekarik with Ashkan Dejagah and the striker almost made an immediate impact but his dangerous low cross was cut out by Aaron Hughes.
The game came to a brief standstill soon after half time when Davies had to receive treatment after clashing with Wolfsburg captain Josue while going up for a header.
Fulham went close to sealing the win just before the hour when Murphy's clever chip played Zamora through.
The Fulham fans held their breath but the striker's first touch let him down and Benaglio came out to stifle his tame shot.
Dejagah was then booked for dissent before Kostner threw on former Newcastle man Obafemi Martins, leaving Wolfsburg with four strikers on the pitch.
Some of the home supporters began to leave with 20 minutes left as Wolfsburg continued to waste possession.
Murphy shot over after turning two defenders while Zamora and Gera continued to pose a threat.
Brilliant
Dzeko then reminded the remaining crowd why he is such a highly-rated player when he forced Schwarzer into a brilliant one-handed save with a volley from the edge of the box.
Simon Davies then beat the offside trap but saw his shot turned over by Benaglio's outstretched leg.
The visiting fans, sensing victory, chanted 'Zamora for England' before the striker had a headed goal ruled out for offside with 15 minutes left.
Fulham had a golden chance to seal the win with 10 minutes left but Murphy's shot was cleared off the line by Barzagli.
Hangeland then scrambled back to clear Grafite's shot off the line after he reacted quickest to Dzeko's shot that had rebounded off a post.
