كتب : Omar AbdelAziz
Despite a disastrous first half, Guus Hiddink's side regrouped in the second period to deny Liverpool, who missed inspirational captain Steven Gerrard.
Chelsea will clash with Spanish titans Barcelona in the semi-finals at the end of the month.
Perfect Liverpool Start
Liverpool couldn't have had a better first half as Brazilian full-back Fabio Aurelio opened the scoring in the 19th minute when he caught Petr Cech napping with a deceiving free-kick from the right flank.
Nine minutes later, another Aurelio freekick saw Chelsea's first-leg hero Branislav Ivanovic pull Xabi Alonso in the area, and the referee had to point to the spot.
Alonso filled in Gerrard's boots to double the Reds' lead in the 28th minute.
Superb Second Half
Six minutes after the break, Didier Drogba met Nicolas Anelka's cross with the slightest of touches, only for Pepe Reina to drop the ball into his own net, thanks to the Ivorian's crucial flick.
Shortly after, another Brazilian was on target with a set piece, this time Chelsea's Alex rocked Stamford Bridge with an absolute screamer from 30 yards.
In the 76th minute, Frank Lampard notched in Drogba's deft low-cross to complicate matters further for Rafa Benitez and Co.
However, the relentless Liverpool hit a quickfire double to find themselves in front again in the 82nd minute.
Lucas' long-range effort was deflected off Michael Essien for the 3-3, before Dirk Kuyt headed in Albert Riera's cross to ensure a pulsating finale.
But the in-form Lampard, who captained Chelsea in the absence of John Terry, denied the Reds once again, finishing off Anelka's layoff with a superlative shot from 18 yards to put the tie to bed.