Alberto Moreno scored the opener a third of the way through the game, converting from six yards after starting and ending a move involving Lallana and Jordan Henderson.
Former Liverpool midfielder Shelvey could have been sent off before half-time after his flailing arm caught Emre Can, but referee Andre Marriner was unmoved.
Two goals in two minutes set the game alight in the second half. First Lallana got in the way of a Lukasz Fabianski clearance for a bizarre second for Liverpool, before Gylfi Sigurdsson slotted home from six yards at the other end.
Lallana extended Liverpool’s lead again, drilling home from 12 yards after a superb assist from Philippe Coutinho, and the Reds were 4-1 up with just over 20 minutes remaining after Henderson’s drilled corner was flicked in by Shelvey for an own goal.
Former Swansea boss Brendan Rodgers set Liverpool up in a 3-5-2 formation with Can one of three centre-backs and one of four changes, but the new look to his side did not dishevel them.
Henderson’s drilled corner found Martin Skrtel at the far post, but the defender’s powerful header from six yards only found the hands of Lukasz Fabianski.
Moreno, who attempted to get forward at every opportunity at wing back, found Raheem Sterling with a drilled cross after 15 minutes, but the Englishman’s powerful volley was straight at Fabianski.
The ball bobbled around the area before falling to Lallana, who disappointingly fluffed his effort over the bar from just 12 yards.
Liverpool went ahead on 33 minutes, with Moreno starting and finishing the move. The Spaniard piled forward from the left of Liverpool’s midfield, offloaded to Lallana who then found Henderson in space on the left, before a drilled centre was converted by Moreno from six yards for his second Reds goal.
The hosts nearly doubled their lead a few minutes later, Coutinho twisting and turning on the byline only to see his low effort saved from the left at the near post by Fabianski.
There was controversy just before half-time when Swansea midfielder Shelvey, returning to his former club, appeared to fling his arm at Can while piling through the Liverpool defence.
The second half began in bizarre fashion after Fabianski’s clearance came off the body of Lallana to loop into the Swansea net for 2-0.
But the visitors went up the other end to halve the deficit just seconds later, Sigurdsson converting from close range after Mamadou Sakho headed the ball into his path.
Liverpool restored the two-goal lead on 61 minutes through Lallana again, getting on the end of a fine flick from Coutinho to glide past two defenders and slot home into the bottom corner from 12 yards.
And it was four with 21 minutes remaining after Shelvey flicked on a drilled corner from Henderson at the near post to leave his own goalkeeper with no chance.
Bafetimbi Gomis hit the bar late on before Wayne Routledge’s effort fizzed just over from 20 yards, but Liverpool were comfortable winners on the night, leapfrogging Swansea to end 2014 on a high.
Liverpool: Mignolet (6), Can (7), Skrtel (7), Sakho (6), Manquillo (7), Moreno (7), Lucas (7), Henderson (7), Lallana (8), Coutinho (8), Sterling (6)
Subs: Markovic (6), Balotelli (6), Borini (6)
Swansea: Fabianski (5), Richards (5), Fernandez (6), Williams (5), Taylor (5), Britton (6), Shelvey (5), Dyer (6), Sigurdsson (6), Routledge (5), Bony (5)
Subs: Rangel (6), Ki (6), Gomis (6)
Man of the match: Adam Lallana