Corners proved decisive as Chelsea scored from two of them to put one foot in the Champions League semi-final.
Liverpool began well but failed to build on an early success and in the end were well beaten.
The Danish linesman had a very liberal interpretation of offside and a couple of times Chelsea almost got through with the Reds defence claiming an infringement.
Both sides were going for goal in more of a typical Premier League game than the first leg of a Champions League quarter final.
The visitors refused to be intimidated by the crowd as Liverpool poured forward with Torres proving a handful.
Gradually the game was becoming more even and it was no surprise when Chelsea drew level just before the break.
Salomon Kalou fired in a corner and defender Branislav Ivanovic rose unmarked to head home past a stranded Reina.
The second half began in frenetic style with Chelsea quickest out the blocks.
Then two goals in five minutes silenced the Anfield crowd.
Ivanovic again was allowed to meet a Lampard corner unmarked, as The Reds failed to heed the lesson's of the first half, and the Serbian's head did the rest.
The killer third goal was a well worked affair involving Michael Ballack and Florent Malouda and when the cross came in Drogba was presented with the easiest of chances from close range.
The home side quickly ran out of ideas and Chelsea comfortably held on for a famous victory.
Blues boss Guus Hiddink freely admitted this result was "unexpected."
"To play at Liverpool and win is always difficult as has been proved in the past with other big teams.
"Obviously we are delighted even if, to be honest, it was unexpected.
"It was well deserved, we started sloppy defensively and conceded. But the team reacted well as always and we know we can score.
"It was also good to see the team go on from 1-1 when it would have been normal sit back and settle for that result. But the team felt it could do more and get a second goal."
"We had an early goal, then they had chances but with five or six players who are good in the air it is difficult to stop them.
"We made mistakes and gave them free headers.
"Now we can only think about the important game on Saturday against Blackburn, but we still have a chance.
"There are ninety minutes still to play and who knows what can happen – it will be very difficult as we have to score three goals."