Chelsea recovered after a Fernando Torres goal had put Liverpool ahead in the sixth minute, stunning the five-times European champions with two headers from Branislav Ivanovic and a hammer-blow third from Didier Drogba.
The result even amazed Chelsea's temporary coach Guus Hiddink, who won the tactical battle with Liverpool coach Rafa Benitez, a master tactician himself, especially in Europe.
"It was very surprising to have scored three, we didn't expect it. But remember it is only halftime, Liverpool have pulled off some remarkable comebacks in the past," said Hiddink, who pulled off a masterstroke of his own by designating Michael Essien to patrol Steven Gerrard and negated the Liverpool skipper's usual influence.
Shackling Gerrard was key to victory - but so was deploying Ivanovic as the target man from two set-piece corners. The Serbian defender had not scored for Chelsea since arriving in January last year.
But the Liverpool defence twice failed to pick him up and he punished them both times with two carbon-copy goals, one in each half.
The second after 62 minutes put Chelsea 2-1 ahead and Liverpool, looking unrecognisable from the side that beat Real Madrid 4-0 at Anfield in the last round a month ago, were shattered when they conceded a third from Drogba five minutes later.
"It is going to be tough, and we have to go there and score three but we can do that," a defiant Benitez said afterwards. "The tie is not over yet."
REMEMBERING ISTANBUL
Even though Chelsea do look set for a semi-final against Barcelona, Liverpool's players are seeking inspiration from their own glorious European history as defender Alvaro Arbeloa told Liverpool's website on Thursday.
The Spaniard said he hopes the side can recreate their heroics from the 2005 Champions League final, when they overturned a 3-0 half-time deficit to draw 3-3 with AC Milan in Istanbul and win the trophy on penalties.
"We can do it - why not? We believe we can. We have to go there and fight, try to get one goal and then think about another.
"Liverpool won a Champions League final by scoring three goals in 45 minutes, so why can't we get three in 90?
"I think we have to remember Istanbul and believe. We know it's going to be difficult to beat Chelsea at Stamford Bridge but it's not over."
Meanwhile, Brazilian Lucas Leiva says Liverpool have already shown they can score goals away from home, as they proved by beating Manchester United 4-1 at Old Trafford last month.
"We know it will be really difficult but it's not impossible," Lucas told the website. "Chelsea came here and scored three, and we have the quality to do the same there. We need the perfect performance."
Chelsea skipper John Terry will miss the second leg after being booked for a barging into Liverpool goalkeeper Pepe Reina.
The Blues will miss Terry enormously but, with three away goals in the bank, next week's match might be a rare one in which they could afford to be without him.
