A first-half strike from Maxi and one from ex-Blue Glen Johnson, three minutes from time consigned the Blues to their fourth defeat of the season and their second in a row at Stamford Bridge.
Chelsea's strike came from the boot of substitute Daniel Sturridge.
The last time Chelsea lost back-to-back matches was in 2005.
The game started with both sides intent on not giving needless possession away. Twice Maxi profited early on from excellent through balls from midfield as the visitors sought to take advantage of Chelsea's high line.
Thankfully for the Blues John Terry and Branislav Ivanovic were alert to snuff out the threats. Chelsea had a sniff of a chance on 10 minutes when Juan Mata got on the end of a Florent Malouda left wing cross, but his sight-footed volley was screwed wide of goal.
Mikel had a long range effort high and wide of Reina's goal a minute later. Petr Cech was alive to the mazy left wing run of Craig Bellamy which almost reaped dividends on 14 minutes.
Chelsea fans thought they had scored on 22 minutes when following a foul, Drogba dusted himself off and sent in a clever free-kick from 20 yards, which left Reina stranded.
Sadly for the home side, the ball inched wide of the goalkeeper's left hand upright. Lucas received a yellow card from referee Lee Probert on 29 minutes after upending David Luiz. Liverpool took full advantage of a terrible Chelsea error on 33 minutes as Liverpool took the lead.
Cech rolled the ball out to Mikel on the edge of his area.
The midfielder was then dispossessed by Adam who, following a swift interchange with Bellamy and Suarez found Maxi free to exploit the gaff to slot the ball wide of Cech from eight yards out.
Ivanovic attempted to right the wrong two minutes later but from a Malouda corner the right-back headed wide of goal.
Liverpool had a great chance to double the lead a minute before the break, when Suarez took full advantage of sleepy Chelsea's rearguard to race through.
However Luiz was quick enough to recover and deflected the shot away from goal for a corner. Chelsea boss Andre Villas-Boas decided to change tact at half-time by replacing Midfielder Mikel for Daniel Sturridge.
Drogba almost equalised three minutes into the second half. Getting onto a Lampard run, the Ivory Coast striker curled the ball high and wide from just inside the penalty area.
Martin Skrtel then hacked away the ball for a corner after Mata looked to be ready to fire the trigger as the Blues pushed forward.
And they got their just rewards on 55 minutes. Liverpool allowed Malouda to run straight through towards the area. the French winger sent in a low left-footer which bisected the visitors' defence and up popped Sturridge with the easiest of chances to tap home from close range at the far post.
Reina then produced a wonder save 60 seconds later, after a Drogba free kick was headed towards goal by Ivanovic.
Reina somehow got low to his left to tip the ball round the goal to safety. Liverpool boss Kenny Dalglish replaced Bellamy with Jordan Henderson on 67 minutes.
Malouda produced a nice piece of skill on 70 minutes, but his overhead kick from a Lampard pass drifted just wide of the target. Malouda somehow managed volley across the Liverpool goal on 76 minutes just before Liverpool's second substitution - Stewart Downing for Maxi.
Ex-Liverpool players Fernando Torres and Raul Meireles entered the fray with six minutes remaining - on for Drogba and Ramires.
Dirk Kuyt had a great chance to score - Liverpool's first of the second half, but his shot was wide. But they got the winner with two minutes remaining.
A long ball by Charlie Adam found Glen Johnson wide on the right, the ex-Chelsea full-back raced in on goal, and sent a low left footer past Cech. Chelsea' s only response - a weak Torres shot and a blaster from Meireles that sailed embarrassingly high and wide.