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 their lacklustre back-to-back draws against Leicester City and West Ham.
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 they beat Chelseaon Sunday. Such fine margins being at play mean Klopp might have liked to see a few more added to their 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 Egyptsuperstar 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.
Your move, Pep Guardiola'
The past week in this gripping, twisting and turning title race has belonged to Manchester City, but the fact remains that if Liverpool win all their games they will be crowned champions.
Pep Guardiola's side now host a Chelsea team who have already beaten them in the top flight this season. On the other hand, Maurizio Sarri's men were demolished 4-0 at Bournemouth 10 days ago – a ninth consecutive away defeat in all competitions confirmed the picture is very different on the road for the Cherries.
Wijnaldum brings classy assurance to Reds midfield
The Netherlands midfielder was one of the players Klopp lost to injury on the eve of Monday's 1-1 draw at West Ham. As in the 4-3 home win over Crystal Palace, which Wijnaldum also sat out, Liverpool lost the control of central areas and were vulnerable to opposition counter-attacks. There were no such struggles with Wijnaldum back in situ and a commanding performance was crowned by a beautifully executed goal.
Ake's Anfield aggravation
Wijnaldum's international team-mate Ake endured a somewhat contrasting outing, allowing his countryman too much room for the champagne moment before being easily bested by Firmino for the third goal. Playing at centre-back at the moment Liverpool rediscovered their briefly misplaced swagger made this a thankless task for Ake.
