Sadio Mane scored for the fourth consecutive top-flight match in the 24th minute, after which point Jurgen Klopp's side kicked into top gear to banish the memory of its lacklustre back-to-back draws against Leicester City and West Ham United.
Mane opened the scoring in both of those games as well, but fabulously worked goals from the returning Georginio Wijnaldum and Mohamed Salah ensured there was no chance of another wobble.
Manchester City will return to the summit on goal difference if it beats Chelsea on Monday (NZDT). Such fine margins being at play mean Klopp might have liked to see a few more added to its tally as his team cut Bournemouth apart at will.
Ryan Fraser forced an early save from Alisson and his inventive attacking meant James Milner had to be on his guard, but the makeshift right-back produced a wonderful cross for Mane to powerfully head home.
Salah uncharacteristically missed his kick at the end of a 28th-minute counter-attack and the increased pressure on Bournemouth's backline told when Andy Robertson picked out Wijnaldum, whose first touch and lobbed finish over Artur Boruc were immaculate.
Boruc palmed a stinging Salah volley over his crossbar in the final minute of the half and all of Liverpool's fabled front three were involved when the Egypt superstar got on the scoresheet in the 48th minute.
Roberto Firmino ran off the back of Nathan Ake to collect Mane's throughball and backheeled for Salah to coolly roll his 20th of the season into the bottom corner.
Mane powered a header wide from Wijnaldum's chipped cross and the excellent Firmino played in Salah to clatter the crossbar in the 7th minute.
Wijnaldum made way for Trent Alexander-Arnold's welcome return from injury, with the England international following Firmino in forcing a fine late stop from Boruc.
Liverpool has 10 days off before hosting Bayern Munich in the UEFA Champions League, with its game in hand on Manchester City coming at Manchester United on 25 February (NZDT).