With one match remaining, Chelsea are five points adrift of fourth-placed Tottenham Hotspur and four behind fifth-placed Newcastle United, both of whom are in a final-day scrap with Arsenal to determine the Champions League qualifiers.
It is the first time Chelsea will have finished outside the top four since the 2001-02 season, although they could still grab a place in next year's Champions League if Roberto Di Matteo's side beat Bayern Munich in this year's final on May 19.
Should that happen, the team that finishes fourth in the Premier League would be deprived of a Champions League qualifying round tie and be bumped down to the Europa League.
Liverpool, smarting from their FA Cup final defeat at Wembley on Saturday, were 3-0 up against a much-changed Chelsea side inside half an hour thanks to a Michael Essien own goal, Jordan Henderson's neat finish and Daniel Agger's header.
Ramires pulled one back for Chelsea five minutes after the break but a mistake by their keeper Ross Turnbull, deputising for the rested Petr Cech, allowed Jonjo Shelvey to fire a sublime shot into an unguarded net from 30 metres just past the hour.
Andy Carroll wasted a chance to extend Liverpool's lead while Agger also headed wide late on.
Liverpool's win saw them leapfrog Fulham into eighth place on goal difference and they can still finish above Everton if their result at Swansea City on Sunday is better than that achieved by their city rivals at home to Newcastle United.
