The game was over as far as Blues were concerned as early as the first four minutes when a clinical Liverpool steamed into a two-goal lead through Sami Hyypia and Peter Crouch.
Crouch, who couldn't score for Liverpool in the early part of the season, is now enjoying a purple patch and added to his second before the break to take his tally for the season to 10.
Shell-shocked Blues, making their first quarter-final appearance in 22 years, were simply out of their depth and their relegation problems overflowed into this cup encounter as Fernando Morientes, John Arne Riise, an own goal from Olivier Tebily and Djibril Cisse completed the scoring.
Even Blues' disappointed fans remained in the ground despite seeing their side suffer such a heavy defeat as they realised they were watching a special side.
The high scoring Liverpool, quoted before the game at 80-1 to win by five goals, took full advantage of some miserable defensive work by the Blues rearguard which possesses one of the worst records in the Premiership.
It was not merely the result but the way but the way Blues capitulated in those miserable opening four minutes that heaps pressure on under-fire manager Steve Bruce.
The chaos, which has been evident in recent Blues games, surfaced after only 55 seconds when a free-kick deep on the left by Steven Gerrard was headed on by Mohamed Sissoko to the unmarked Hyypia to head home from close range.
Before Blues had any time to regain their brittle composure they slumped even deeper into trouble when a Gerrard cross from the right was headed home by Crouch as Maik Taylor fumbled the ball.
It was a performance of a demoralised side against a team rapidly hitting top form and as a result the outcome was never in any doubt.
Liverpool, who have now scored 15 goals in their last three games, took their foot of the pedal after being given such a generous lead.
They settled down to produce some skilful football as Blues battled to repair the damage without any success.
But it was significant that Jose Reina was never tested by the Blues attack in which Mikael Forssell was often used as a lone striker.
In the 37th minute Crouch popped for his second goal when he took advantage of Blues' easily penetrated defence to latch on to a Harry Kewell pass to slot a low shot past Taylor.
One distraught Blues fan even invaded the pitch to give vent to his feelings and had to be escorted off by security officials.
Liverpool took off Crouch in the 55th minute but it made no difference as his replacement Morientes moved on to an unselfish pass from Gerrard four minutes later to glide home the fourth goal.
But the best goal came from Riise who scored in the 70th minute with a screaming 30-yard rocket shot past the helpless Taylor who was beaten again in the 78th minute by Tebily's own goal and by Cisse in the last minute as Blues were over-run.