It was 4-3 to Liverpool with seven minutes of normal time remaining and Stamford Bridge was stunned, while the Reds required just one more goal to complete a sensational victory on away goals.
But Lampard converted Nicolas Anelka's pass to level at 4-4 in the final dramatic action of a truly memorable game of football.
Liverpool were without their skipper Steven Gerrard because of an injury but came close to pulling off a memorable victory without their inspirational leader.
We were angry at half-time - Hiddink
Liverpool gave the hosts an early warning when a delightful touch from Yossi Benayoun after 13 minutes created a clear opening for Fernando Torres, who failed to hit the target with his left-foot strike.
It was a poor miss and Liverpool's slim hopes were almost completely extinguished a minute later but Lampard narrowly missed the target with a free-kick.
Then came the moment that embarrassed Cech and handed Liverpool a lifeline, as Aurelio smashed his free-kick into the bottom corner.
Alex celebrates with Michael Ballack after scoring Chelsea's second
Chelsea had only bothered to put one man in the wall and Cech was so focused on dealing with a floated ball into the congested area that he neglected the possibility of a low shot at goal.
Even so, it was a terrible error as the Czech keeper was caught completely out of position and scrambled across goal in vain.
Buoyed by their goal, Liverpool suddenly found an incisiveness and rhythm to their play, while Chelsea, with suspended skipper John Terry watching from the stands, looked uncharacteristically brittle.
Terry will be back for the semi-final first leg tie against 2006 champions Barcelona at the Nou Camp in two weeks, but left-back Ashley Cole will be absent after picking up a yellow card for a foul on Alvaro Arbeloa.
The Blues defensive unit struggled to cope with the passing and movement of an attacking line that had struggled so manifestly at Anfield eight days earlier.
We did a fantastic job - Benitez
And the Reds doubled their lead through Alonso's unstoppable penalty after the Spaniard had been fouled by Chelsea's first-leg hero Branislav Ivanovic.
Chelsea boss Hiddink withdrew Salomon Kalou and brought on Anelka after 35 minutes.
And his bold decision was vindicated when the Frenchman's low cross from the right shortly after the restart was deflected by Drogba past Liverpool keeper Reina, who could only parry the ball into his own net.
Drogba was inches away with a free-kick as Chelsea found the attacking menace that had almost completely eluded them in the first-half and it came as no huge surprise when they did draw level, Alex drilling home his long-range free-kick.
Kuyt's goal gave Liverpool renewed hope of a famous result
Liverpool now needed to score twice more but Michael Ballack should have put the result beyond doubt after Drogba broke down the right and picked out the unmarked German with a precise low cross. Ballack, however, shot tamely and Reina dived to his left to save.
Torres, an increasingly marginal figure, went close from distance but it was Chelsea who were in control now and Lampard put his team ahead with a close-range finish from Drogba's cross.
The tie seemed to be dead and buried before Lucas' deflected strike after 81 minutes was quickly followed by Kuyt's bullet header from substitute Albert Riera's cross.
Suddenly it was only the visiting supporters who could be heard but the final goal of a pulsating match fell to Lampard, whose strike went in off both posts.
There was hardly any time remaining but the fragile Cech still managed to fumble a cross that David N'Gog drilled towards goal, forcing a superb headed clearance from Michael Essien.
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