Liverpool, who had managed only a draw in their three previous outings, broke the record for the highest-ever Champions League victory margin held by Arsenal and Juventus.
England striker Peter Crouch gave the Reds the lead before Israeli international Yossi Benayoun took centre stage with his first Champions League goal on the half hour.
He added two more within the space of three minutes in the 53rd and 56th minute, opening the floodgates in the process. Captain Steven Gerrard made it 5-0, then substitute Ryan Babel added another two to equalize the record margin.
Crouch ensured that the evening ended as it had begun, with his second goal on the night to put his club into the records book.
Coach Rafael Benitez said that they had gone into the game knowing that they needed to win. "The players knew that they had to give everything and they showed true character and class.
"Once we scored the first goal, that took a lot of pressure off us and once we started scoring it seemed easy."
He said however, that the victory was only a small step towards qualifying for the next round. "We need to win the next to games to go through. Let us see what the situation is at the end of those two matches."
The win takes the Premiership side to four points in Group A, three behind Olympique Marseille and four behind Porto, who beat the French side 2-1 in Portugal with goals by Moroccan Tarik Sektioui and Lisandro Lopez, while Mamadou Niang scored for the visitors.
In Group B Norwegian club Rosenborg Trondheim took a giant step towards qualifying for the knock-out stages with a 2-0 win in Valencia, while Chelsea played to a goalless draw at Schalke 04 in Germany.
The Premiership side top the group on eight points, one more than Rosenborg, while Schalke have four points. Valenica are last with three points from their three games.
In Valencia former Tottenham player Steffen Iversen scored both goals for Rosenborg.
Group C remains wide open after leaders Real Madrid were held to a goalless draw in Athens by Olympiakos, who ended the game with ten men, while Serie A side Lazio beat Werder Bremen 2-1.
Tommaso Rocchi scored twice in the second half for Lazio, while Brazilian midfielder Diego, who was sent off in injury time, scored from the spot for the Bundesliga side.
Real Madrid has eight points, three more than Olympiakos and Lazio, while Werder Bremen have just three.
In Group D AC Milan, who won 3-0 at Shakhtar Donetsk through two second-half goals by a Filippo Inzaghi brace and Kaka, took a giant step towards the next round.
The Serie A side have nine points, while Celtic, who beat Benfica Lisbon 1-0, have six, as do Donetsk. Benfica, who ended the game in Glasgow with ten men after Cameroonian midfielder Gilles Binya was sent off for a horrendous tackle on Scott Brown, have three points.