Goals from Philippe Coutinho, Dejan Lovren and Mohamed Salah gave the Reds a commanding lead before half-time, as the hosts struggled to counter the Anfield giants' threat.
Roberto Firmino grabbed a fourth in the second half, and there was no way back into the contest for the home side.
Andrew Robertson maintained his place in Liverpool's starting line-up, as manager Jurgen Klopp once again relied on his sumptuous attacking unit.
Jermain Defoe led the attack for the Cherries, but it was a difficult day at the office for the veteran No. 9.
Liverpool were out of the traps in a flash during the first half, with the hosts flooded by a barrage of quick movements.
The opening goal came for Klopp's men after 20 minutes as Robertson linked with Coutinho for the Brazil international to score.
The left-back's marauding run from deep opened up the defence for Coutinho, and the 25-year-old furthered his world-class reputation with a sublime run and finish.
Klopp was jubilant as he watched his side hit their maximum on the front foot, and they doubled their lead just six minutes later.
Firmino chased a lost cause, and his lofted cross was met by an accurate diving header from Lovren.
Bournemouth appeared stunned by Liverpool's appetite, but they came close to pulling a goal back as Defoe hit the post.
The miss was punished on the stroke of half-time as the Reds scored their third, with Salah dribbling into the box and finishing with aplomb.
B/R Football highlighted the player's amazing season for his new club:
Bournemouth simply could not find a way into the match after the restart for the second half, and despite a more conservative approach, the visitors made it 4-0 after 66 minutes.
Firmino ghosted into the penalty box to beat the offside flag, glancing home a magnificent header to kill the match.
The attacker has impressed as a No. 9 under Klopp's guidance, and when Liverpool click as they storm forward, Firmino is a consistent threat.
Liverpool were comfortable in the closing stages, and the Cherries were well beaten as their fans continued to faithfully watch the action.
Football writer and Liverpool supporter, Carl Clemente, tipped his hat to Klopp's side:
However, Liverpool remain 18 points behind runaway Premier League leaders Manchester City.