Goals from returning trio Alex Oxlade-Chamberlain, Naby Keita and Mohamed Salah in a devastating 19-minute spell either side of half-time did the damage for the relentless Reds, who lengthened their club-record top-flight unbeaten streak to 33 matches.
Jürgen Klopp’s team have now amassed 46 points from a possible 48 in the division this season, with their cushion at the summit growing due to second-placed Leicester City not being in action until Sunday.
Curtis Jones made his Premier League debut as a 76th-minute substitute on a day where the only obvious negative was the enforced withdrawal of Dejan Lovren, who had to be replaced due to injury in the first half.
Team news
Klopp made seven changes to his starting line-up, with Alisson Becker, Joe Gomez, Jordan Henderson and Roberto Firmino all coming in along with goalscorers Oxlade-Chamberlain, Keita and Salah.
Georginio Wijnaldum and Adam Lallana missed out due to minor knocks.
First half
Liverpool quickly settled into their rhythm, the visitors monopolising possession in the early stages by recycling the ball while seeking an opening.
Their first effort on goal arrived with seven minutes on the clock. Gomez found Salah with a clever pass inside, but the No.11’s attempted curler into the far top corner was fielded by Aaron Ramsdale.
The Reds’ front-foot approach was maintained throughout the first 20 minutes, but their final pass lacked incision as Bournemouth sat in with plenty of men behind the play.
A first foray forward of note by the hosts saw a shot by former Liverpool striker Dominic Solanke deflected wide by Lovren, before James Milner directed an attempt narrowly off target following a neat one-two with Salah.
Eddie Howe’s side appeared to gain confidence for a period and Virgil van Dijk’s perfectly-timed sliding tackle thwarted Solanke after Keita had been pick-pocketed by Ryan Fraser in midfield.
Nathan Ake replicated his international teammate at the other end to dispossess Salah, who had latched onto Keita’s through-ball, but the centre-back hurt himself while doing so and had to be replaced.
And within a couple of minutes of that change, Liverpool had the lead, with Oxlade-Chamberlain’s stretching volley beating Ramsdale from Henderson’s marvellous raking pass.
Injury then induced another substitution, this time for the Reds as Lovren was withdrawn for Trent Alexander-Arnold.
Despite that disruption, the visitors subsequently shifted through the gears and deservedly doubled their advantage prior to the break when Keita collected an ingenious backheel by Salah and slotted in from close range.
Salah himself could have furthered Bournemouth’s pain in stoppage time, but the Egyptian failed to convert at the back post after Firmino had flicked on Alexander-Arnold’s corner.
Second half
The assurance that characterised Liverpool’s play in the closing stages of the first period was again in evidence immediately after the restart.
Ramsdale got down well to save a snap-shot volley by Keita, but the Bournemouth goalkeeper was beaten again nine minutes into half as the No.8 returned the favour for Salah.
Keita intercepted Jack Simpson’s wayward pass and slipped in his teammate, who duly dispatched a cool, clinical finish into the far bottom corner.
Ramsdale denied Salah - a goalscorer for the fifth game in succession versus the Cherries - when the forward ran onto Henderson’s pass and blasted at goal, but Liverpool continued applying pressure with a persistence that belied how comfortable the scoreline had become.
Jones nearly capped an impressive cameo with a goal, the young Scouser’s left-footed volley from 20 yards clearing the crossbar, but the Reds had already done more than enough in a consummate, dominant display.