It had all seemed so different in the opening minutes when Fernando Torres put the Reds ahead but Guus Hiddink's side responded superbly and thoroughly deserved their win.
It was the fifth successive season that the two teams had met in the competition but it now seems as though it will be Chelsea who will be playing Barcelona in the semi-finals this time.
Liverpool had already beaten Chelsea twice in the Premier League this season, but it was a very different story this time.
The match started at a frenetic pace and, in the fourth minute, Steven Gerrard's corner was headed out by Alex straight to Dirk Kuyt who fired in a shot that was only narrowly wide.
However, two minutes later Rafa Benitez's side went ahead. Kuyt found Alvaro Arbeloa galloping down the right and Torres was on hand to turn the excellent cross home.
Almost immediately Drogba should have brought Chelsea level but, after some dithering in defence by Liverpool, the Ivorian striker slammed his shot straight at Pepe Rena.
When the Reds responded midway through the first half, Frank Lampard was caught in possession by the alert Torres. The Spaniard saw Petr Cech off his line and was only just too high with an ambitious lofted attempt on goal.
Two minutes later Drogba wasted another great chance to equalise. Michael Ballack found him inside the penalty area but, from just ten yards out, the forward lashed a shot way over the bar.
Six minutes before the interval Chelsea did eventually score when Ivanovic got ahead of Martin Skrtel and powered a header past Reina.
Straight from the restart Liverpool almost regained the lead. Kuyt sped past John Terry but Cech made a great save to deny the Dutchman as a scintillating first half of football that could easily have seen a hatful of goals came to an end.
The second half was all Chelsea's though as they stepped up the pace.
In the 52nd minute poor defensive play by Fabio Aurelio let Drogba in again. This time the striker's effort was on target but Jamie Carragher was on hand to clear the ball off the line.
Three minutes later, when play swung to the other end, Torres, under pressure from Alex, lifted his shot high and wide. It proved to be a costly miss as two goals in five minutes effectively ended the match as a contest.
In the 62nd minute Chelsea moved ahead with a carbon-copy of their first goal as Ivanovic rose highest to head another corner past Reina.
Five minutes later the visitors put together a superb move as Ballack found Florent Malouda whose cross was rifled into the net by the previously wasteful Drogba.
Chelsea's only black mark on a fantastic evening for them was Terry's yellow card for a challenge on Reina which means he will be suspended for the second leg at Stamford Bridge next Tuesday.