The Gunners started in sensational style, displaying blistering pace, strength in the tackle and sublime passing skills.
Alexander Hleb, in a central role supporting Adebayor, was a constant danger and they were ahead in the 13th minute.
Anfield was stunned into silence as Hleb threaded a ball down the right for Diaby to surge into the box before crashing home a shot between Jose Reina and his near post.
With Gerrard deployed on the left, Arsenal were destroying Liverpool's midfield, and flying at a frantic defence.
They were handed a lifeline when the 34-year-old Hyypia produced a towering header from Gerrard's corner after completely losing marker Philippe Senderos.
Suddenly Liverpool were alive. Gerrard flashed a 30-yard shot wide, Dirk Kuyt's drive was charged down and Senderos - already booked for a foul on the Liverpool captain - started to struggle against Crouch's height.
Then Arsenal suffered the blow of Mathieu Flamini being carried off after looking to have fallen awkwardly on an ankle.
Gilberto came on after 40 minutes. By now Liverpool looked a changed side; steaming forward, their confidence restored.
England boss Fabio Capello and Manchester United chief Sir Alex Ferguson sat side by side as Arsenal steeled themselves to defend in front of the Kop after the break.
Fabio Aurelio's shot was deflected agonisingly wide by Crouch, Torres having provided the cross.
It was the Spain striker, quiet up to that point, who forced Liverpool ahead. Crouch's flick-on reached the Liverpool goal machine in the box, he turned Senderos with ease before firing his shot into the top corner.
Wenger replaced Diaby and Emmanuel Eboue with Robin Van Persie and Theo Walcott, knowing another Arsenal goal would put them through.
Adebayor missed when clean through, the tension by now could be cut with a knife. Babel then came on for Crouch, who left the field to a standing ovation.
Liverpool switched back to their preferred system, with Gerrard working behind Torres while two holding players protected the midfield.
But Liverpool were caught searching for more, and Arsenal caught them cold on the break.
Walcott embarked on an amazing run from his own half before pulling the ball back for Adebayor to drill in the equaliser after 83 minutes.
But astonishingly they rallied. Straight from the restart, some Gunners still celebrating, Babel surged into the box and was brought down by Kolo Toure, for what looked a soft penalty.
Swedish referee Peter Frojdfeldt pointed to the spot, and with the Kop in hushed agony, Gerrard drove the penalty high into the net.
John Arne Riise came on for Torres with Liverpool desperate for the end now as another Gunners goal would again see them through.
But with Arsenal all up in Liverpool's box for a free-kick, the ball broke from the mass of players to be belted forward for Babel to outpace Fabregas to drive home the fourth.
Alvaro Arbeloa came on for a shattered Kuyt, and there was nothing left now from Wenger's men as Anfield celebrated.
Yay!
