But it was Fulham, needing two goals to win, who dramatically took the lead late in the second-half to earn their place in the May 12 final.
Davies controlled a fierce pass from fellow midfielder Danny Murphy late into the game, cutting inside defender Guy Demel and guiding a left foot shot in off the post.
|Forlan scored again to condemn Liverpool to a fourth season without a trophy [Reuters]
Six minutes later, Davies' outswinging corner rebounded off Hamburg's Demel towards Gera, who swivelled and fired home from eight metres.
"It just keeps getting better doesn't it," Fulham captain Danny Murphy said.
"It would have been easy to think this was the end of the journey, but I thought the spirit we showed in the second half was tremendous."
Match-winner Gera said: "That was the most important goal I've ever scored, so I'm very happy."
Fulham also beat Bundesliga champions VfL Wolfsburg, Italian giants Juventus and 2009 UEFA Cup winners Shakhtar Donetsk earlier in the competition.
Fulham manager Roy Hodgson said: "The character of this team has been proved time and time again, but they consistently surprise me with the way they keep going.
"If you saw the way they were running around in the second half you would never know we have played 59 games in this season."
A crucial away goal from Atletico Madrid's Diego Forlan denied Liverpool a place in what would have been an all-English semi-final.
Liverpool made two changes to their starting line-up from last week's first leg as Sotiros Kyrgiakos was replaced by unsettled Italian midfielder Alberto Aquilani, with Javier Mascherano dropping into the back four, and Ryan Babel coming in for the injured David Ngog.
Trailing 0-1 after a first-leg Forlan goal in Spain, Aquilani netted in the 44th minute after a clever looping pass from Lucas.
A fast-paced second half set up extra-time and the hosts took a 2-0 lead on the night through Yossi Benayoun's angled strike only for Forlan to smash the ball home a few minutes later.
The Uruguayan striker's goal condemned the five-time European champions to a fourth season without a trophy.