Birmingham went into the tie as the only Premiership team Liverpool had not beaten since Rafael Benitez became manager. That anomaly was consigned to history within 3min 56sec, by which time it was already 2-0. Steven Gerrard was at his inspirational best, playing a part in goals by Peter Crouch (two), Sami Hyypia, Fernando Morientes and John Arne Riise.
Birmingham's misery, compounded by the sight of a pitch invader being led away before half-time after he tried to confront Steve Bruce by his dug-out, continued after Gerrard was substituted. An own goal by Olivier Tebily made it six and a soft seventh for Djibril Cissé all added up to Liverpool's biggest away victory in the competition.
Bruce spoke afterwards of his "worst night in management" and the heaviest defeat since primary school. "I'm shell-shocked, disappointed and humiliated," he said. "Sometimes football kicks you in the teeth - and that is the biggest one I have taken. It was men against boys. We were two down before we'd had a kick. But it has been coming. Too many of our big players are sitting in the stand, injured."
After promising to have "a good look at myself", he was asked whether he was confident he still had the board's backing. "You'll have to ask them," he said. "After a defeat like this, of course questions will be asked. I won't take anything for granted, but my relationship with the board has always been good. I still think I'm the right person to pull us through. I accept responsibility, but I'm not a quitter. I'll do my best to keep us in the Premiership."
Bruce sought to strike an optimistic note, adding: "One thing in this game - there's always another match around the corner."
Birmingham's next game is away to a Manchester United team with five consecutive wins to their name. The following Saturday they are at home to the champions-elect, Chelsea.
Benitez, himself looking forward to the weekend derby against Everton, was careful not to gloat. "I've been in charge of teams who have conceded four or five, and it's very difficult," the Liverpool manager said before purring about his side's "fantastic" and "professional" performance.
The first goal, after 52 seconds, was especially sweet for Momo Sissoko. Returning a month after sustaining an eye injury that was thought to be sight-threatening, the Malian wore red-rimmed, Edgar Davids-style goggles. That did not prevent his glancing on Gerrard's free-kick for Hyppia to head home.
Sissoko soon initiated the second goal by sweeping the ball wide to Gerrard, whose cross found Crouch darting in front of Kenny Cunningham to make a stooping header past Maik Taylor.
Gerrard, whose participation 48 hours after the victory at Newcastle had led Benitez to complain about the over-working of England's World Cup players, looked anything but jaded as he ran amok. The origins of Liverpool's third goal lay in their captain's flick-on from a Steve Finnan throw. Luis Garcia raced through unopposed before slipping a pass to Crouch, who hit his 13th goal of the season from 12 yards.
Crouch's hat-trick hopes were dashed when Benitez sent on Morientes, who joined the spree. It was scant consolation to Birmingham that the build-up befitted Liverpool's status as European champions. Finnan launched it with a pass that Luis Garcia dummied. Gerrard drove into the area, his pass giving the Spaniard a simple finish.
Mikael Forssell finally tested Jose Reina in the 63rd minute but within seven minutes, Riise's fulminating drive from 25 yards left Maik Taylor clawing air, and Liverpool were still not sated. Trickery by Kewell panicked Tebily into slicing the ball into his own net and Maik Taylor's nightmare was complete in the final minutes when Cissé's shot passed under his body.