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Visiting forward Antoine Semenyo saw an early strike overturned for offside following a VAR review before one-way traffic ensued in the first half at Anfield, with Diaz twice on target.
The Colombia winger profited from Kepa Arrizabalaga’s slack positioning for the opener before finishing through the legs of the Bournemouth goalkeeper just 2mins 2secs later.
Darwin Nunez added an eye-catching third with a brilliant strike before the break as Arne Slot’s side responded in style to their 1-0 defeat against Nottingham Forest last time out in the competition.
Saturday’s routine win moves Liverpool, at least temporarily, to top spot before Sunday’s heavyweight encounter between Manchester City and Arsenal, while Bournemouth drop to 13th spot.
How the match unfolded
The Anfield crowd were silenced just three minutes in after Semenyo turned home Justin Kluivert’s cross, only for the goal to be overturned for offside after a VAR review.
That wake-up call kicked the Reds into gear, though, with Diaz rounding the onrushing Kepa and finishing after bringing down Ibrahima Konate’s long punt forward on 26 minutes.
Diaz fired a second past Kepa soon following Trent Alexander-Arnold’s driving run, for the latter’s 100th goal involvement in all competitions for Liverpool (81 assists, 19 goals).
Nunez then curled a wonderful left-footed effort only nine minutes later as Slot’s side went in 3-0 up at the break.
Liverpool were unable to add to their tally in the second half, with Mohamed Salah going closest with a low effort that was cleared off the line by Milos Kerkez.
Andoni Iraola’s Bournemouth almost found a late consolation when Luis Sinisterra twice tested Caoimhin Kelleher – the second of the chances deflecting off the crossbar as Liverpool fortuitously preserved their clean sheet.
Ruthless Reds return to form
Powered by their superstar frontline, Slot’s side rediscovered the form from before the international break, backing up a fine victory over AC Milan in the UEFA Champions League in midweek.
Semenyo’s disallowed strike proved an early warning, though Diaz soon forced a smart Kepa save from distance before the Bournemouth goalkeeper thwarted Salah when one-on-one after Alexis Mac Allister’s stunning pass.
Kepa’s questionable positioning when attempting to cut out Konate’s long ball created Diaz’s well-taken opener, before the Colombian produced another confident low finish after Alexander-Arnold’s marauding inside run.
Nunez capped a ruthless first-half display in style after being played through in a give-and-go with Salah, and that dominance allowed Slot to further flex his attacking muscle in the second half.
Cody Gakpo and Federico Chiesa were both introduced, with the latter making his Premier League debut and testing Kepa with an optimistic volley that would have marked a dream start to life at Anfield.
Leaving Diogo Jota on the bench throughout, Slot has attacking options in abundance as Liverpool prepare to further boost their title credentials in their next league trip to Wolverhampton Wanderers.
Strong showing, but another defeat for Iraola
While the scoreline suggests a comfortable outing for Liverpool, Bournemouth had their moments that made the encounter a tricky affair for the hosts to navigate.
Semenyo’s disallowed opener was a sign of their intent to earn a first Premier League win against the Reds at Anfield, and the Bournemouth forward went close again when rushing a close-range chance against Kelleher, starting in place of injured No 1 Alisson.
Evanilson also proved to be a nuisance at the top end of the pitch, but the former Porto forward lacked support for large parts when up against Konate and Virgil van Dijk.
Dango Ouattara’s half-time introduction injected the pace that was lacking in Iraola’s attack, though, with his trickery causing Alexander-Arnold several problems and forcing a more cautious approach from the attacking full-back.
Sinisterra and Alex Scott both troubled ‘keeper Kelleher late on with Bournemouth’s best chances, but the early damage proved too much after Liverpool thrived against the struggling two-man midfield of Lewis Cook and Ryan Christie.
For all of the Cherries’ promise, it is now one win in their last eight Premier League matches for Iraola, though he will hope to change that at home to Southampton next Monday.
Club reports
Liverpool report | AFC Bournemouth report
Match officials
Referee: Tony Harrington.  Assistants: Marc Perry, Derek Eaton. Fourth official: Bobby Madley. VAR: Graham Scott. Assistant VAR: Sian Massey-Ellis.
PREMIER LEAGUE