Their opponents at the end of the month will again be Chelsea who they defeated at the same stage in 2005 and last season.
In a match that will rank as one of the best ever played in European competition, Liverpool came back from the dead after Arsenal appeared to have clinched the tie on away goals with only six minutes to play.
But Liverpool's indefatigable belief in themselves on European nights at Anfield saw them turn the tie with Steven Gerrard smashing home an 85th minute penalty and substitute Ryan Babel wrapping up a memorable win with a stoppage time goal.
Arsenal, who were superb for the opening half hour playing football worthy of European champions, took the lead through Abou Diaby after 13 minutes.
Liverpool fought back with a header from Sami Hyypia on the half hour and a stunning shot on the turn from Fernando Torres in the 69th minute to give Liverpool a 2-1 lead on the night and 3-2 on aggregate.
A breakaway by substitute Theo Walcott which saw him skate past four Liverpool players six minutes from time set up Emmanuel Adebayor to make the score 2-2 -- 3-3 on aggregate and Arsenal ahead on away goals.
Liverpool got a lifeline a minute later when Arsenal defender Kolo Toure tripped Babel to concede a penalty and Gerrard, who had not had the best of games, scored to put Liverpool 3-2 ahead.
Babel sealed the win with his stoppage time goal to finally ease the tension at Anfield which was almost unbearable throughout an absorbing, enthralling encounter.
BLISTERING START
Arsenal made a blistering start, putting Liverpool under pressure from the kickoff with Alexandr Hleb and Cesc Fabregas taking control of the midfield.
Liverpool coach Rafa Benitez appeared to have got his team selection wrong by playing skipper Gerrard wide out on the left.
The strike partnership of Fernando Torres and Peter Crouch also failed to click at first and it was not until Gerrard moved into a more familiar central position after 25 minutes that Liverpool began to come back into the game.
By then the visitors, who had to score to have any chance of advancing following last week's 1-1 draw at the Emirates in the first leg, were a goal ahead and looking unassailable.
Hleb set Diaby up to score with a powerful angled drive from the right which flew off Liverpool goalkeeper Pepe Reina's thigh and into the net.
Liverpool equalised after 30 minutes when Arsenal left Hyypia unmarked at a Gerrard corner and the tall Finnish defender powered a header inside the far post.
Torres, who had had a relatively quiet match by his own standards, produced a moment of brilliance after 69 minutes, turning and shooting high into Manuel Almunia's net to put Liverpool 2-1 ahead. It was his 29th goal in only his 40th match for the club and sent The Kop absolutely wild.
The game swung back Arsenal's way when Adebayor scored, before Liverpool's stupendous comeback in the closing minutes.
Chelsea scramble to Champions League semi-final
Chelsea reached their fourth Champions League semi-final in five seasons on Tuesday when goals from Michael Ballack and Frank Lampard gave them a nervy 2-0 win over Fenerbahce. The LOndon side's 3-2 aggregate win set them up for a third semi-final clash in four years with Liverpool, who beat Arsenal in the other quarter-final played on Tuesday.
Liverpool won both their previous encounters.
Avram Grant's side had suffered a surprise 2-1 first-leg defeat in Istanbul a week ago against the first Turkish team to reach the quarter-finals.
They attacked early to put things right and when Ballack rose at the near post to head home a free kick from Lampard in the fourth minute, victory looked straightforward.
Joe Cole hit the post in the eighth minute and Didier Drogba also came close early on but the game then descended into frantic but rather messy midfield action. Chelsea had to rely for most of the match on third-string goalkeeper Henrique Hilario after Carlo Cudicini appeared to pull a hamstring and was substituted in the 25th minute. First choice keeper Petr Cech could not play after suffering a face injury that required stitches and plastic surgery in a freak training accident.
Fenerbahce's best chance of the first half came in the 31st minute when Uruguayan defender Diego Lugano rose unmarked in the Chelsea area to meet a free kick but he headed wide.
DROGBA CHANCE
Drogba should have put Chelsea further in front two minutes into the second half but his shot from a neat pass by Michael Essien was scooped up by Volkan Demirel in the Fenerbahce goal. Chelsea remained jittery and Fenerbahce coach Zico upped the pressure 15 minutes into the second half, sending on former Chelsea forward Mateja Kezman for midfielder Claudio Maldonado to try to force an equaliser.
The Turks pressed forward, causing nervous moments in the Chelsea defence. In a frenzied last 10 minutes, Hilario tipped a shot from Ugur Boral round the post and then saved from Kazim Kazim.
But Lampard finished it off for the London side with three minutes to go when, on the break, Essien rounded two defenders on the right of the area and laid the ball through to the England midfielder who scored from point blank range. Essien will miss the first leg against Liverpool through suspension after picking up a yellow card.