Substitute Andrea Dossena completed the rout with two minutes remaining to seal a nightmarish first visit to Anfield for nine-times European champions Real Madrid who limped to another early exit with barely a whimper.
While Liverpool underlined their credentials as UEFA's top ranked team with another special night on Merseyside, Real were left to contemplate a fifth consecutive failure to reach the quarter-finals of a competition they once made their own.
"When you play against Real Madrid you expect it to be tight," Liverpool manager Rafael Benitez, a Real fan and former youth team coach at the Bernabeu, told reporters.
"But we played really well. Away we played fantastic, and today we showed them that we can play in different ways.
"We are top of the European rankings because the last five years were good and this was another good game."
The crushing nature of the defeat did little for short-term coach Juande Ramos's hopes of still being in charge of Real next season.
"We tried to take the game to Liverpool but they were too good tonight. They deserved to go through," he said.
There was a slice of luck about Liverpool's second when Gabriel Heinze was harshly adjudged to have handled the ball by referee Frank de Bleeckere after 28 minutes and Gerrard walloped the resulting spot kick past the dive of Casillas.
Chelsea rode their luck to reach the Champions League quarter-finals on Tuesday with a 3-2 aggregate victory after a controversial 2-2 draw at 10-man Juventus.
Striker Didier Drogba netted from close range on 83 minutes to make sure of qualification after they had twice gone behind.
Juventus, who lost defender Giorgio Chiellini to a second yellow card on 70 minutes, went ahead after 19 minutes when surprise starter Vincenzo Iaquinta smashed home after David Trezeguet's superb through ball.
Michael Essien, starting his first game since injuring cruciate ligaments in Septe
