Liverpool and Chelsea charge into quarters
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.
But for several fine saves by Casillas they could have been staring at a far worse defeat than the 5-0 hammering at AC Milan 20 years ago which still stands as their worst defeat in Europe.
"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.
Ramos, sacked by Tottenham Hotspur earlier this season, complained about a harsh penalty award but his side were comprehensively outplayed.
Cassillas had already saved from Torres and Javier Mascherano when, after 16 minutes, Real defenders Pepe and Fabio Cannavaro both made a hash of attempted clearances, allowing Dirk Kuyt to square for Torres to tap into an empty net.
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.
The tie was all but over by halftime and Gerrard heaped more misery on Real almost immediately after the break when he thumped a half-volley past Casillas from a cross by Ryan Babel.
Both Gerrard and Torres were substituted to standing ovations before Dossena rifled a shot past 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