Liverpool are top of the league. But if that may only be for a day, more significantly, Liverpool are back on track. The tame home defeat to Nottingham Forest looks more of a one-game anomaly. After three goals in San Siro came three at Anfield. As Bournemouth were beaten, like AC Milan before them, a week that began badly for Arne Slot has featured an impressive response.

And a success story of his fine start again illustrated Slot’s early impact. When the final whistle blew, Erling Haaland remained the Premier League’s runaway top scorer. So far, so predictable. What rather fewer would have expected when the season started was that Luis Diaz was his closest challenger. At times in his Liverpool career, the Colombian had provided everything but the goals. Now he has five in as many league matches for Slot: that average of one per game comes after a return of worse than one every four for the club before then.

A win made in South America also included Darwin Nunez’s first for Slot, as he made his maiden start under the Dutchman. But it was determined by Diaz’s two-minute double. Cody Gakpo was terrific against AC Milan but, four days later, Diaz was restored to the team. The destroyer of Manchester United was similarly dynamic. There is a thrilling directness to Diaz, an explosiveness that stems from a willingness to run beyond defenders, to let fly from both long distances and acute angles. What there had not always been was an end product.

But Slot has voiced his confidence that his forwards always score. Diaz may be used to support his case. He had already started tormenting Julian Araujo before a swift brace showed his ability to escape from the right-back.

His opener was remarkable. The 70-yard ball represents a rarity, especially as an assist. Ibrahima Konate provided the sort of pass it seemed only Trent Alexander-Arnold could play. Diaz was the beneficiary, Kepa Arrizabalaga was embarrassed, rushing into no-man’s land as Diaz darted beyond the defence to take down a Konate pass that sailed over the other 18 outfield players, evade the goalkeeper and beat the retreating Araujo with his shot.

Then came an actual Alexander-Arnold assist: a driving, diagonal run began in his own half, ended with him having the composure to find the unmarked Diaz, who slotted his shot under Arrizabalaga.

By that stage, an afternoon that began well for the world’s most expensive goalkeeper had taken a turn for the worse. The on-loan Chelsea player had saved from each of Liverpool’s front three inside a quarter of an hour, denying Diaz again following a scintillating surge.

At fault for his first, he looked culpable again when beaten by a rocket from the right flank from Nunez, fired with his left foot. It raised questions about Bournemouth’s wisdom in dispatching Neto on loan to Arsenal to bring in Arrizabalaga. Liverpool ended with 13 shots on target, but the issue was not Arrizabalaga’s save percentage.

For Nunez, there could be relief a drought had ended. This was his first goal in 15 Liverpool games: even the previous one came from charging down a clearance against Sheffield United. With Diogo Jota rested, he took his opportunity.

Liverpool’s vibrancy could have yielded more goals. Mohamed Salah had a shot cleared off the line by Milos Kerkez. Federico Chiesa came on for his home debut and struck the foot of the post, albeit when the offside flag was raised.

The first to find the net, however, were Bournemouth. Liverpool had an early reprieve when Antoine Semenyo was marginally and needlessly offside before he touched in Justin Kluivert’s low cross. Thereafter, Bournemouth, who lost 9-0 at Anfield two seasons ago and have a lone point on the ground in their history, may not have been surprised at what followed.

Bournemouth went 2-0 down on their previous trip to Merseyside and recovered to win 3-2. This time, they went 2-0 down and were soon 3-0 behind. There was no coming back; this was not Goodison Park. Liverpool are not Everton.

And fresh from a Premier League game with a record number of yellow cards, Bournemouth had Ryan Christie booked within 25 seconds and manager Andoni Iraola cautioned for dissent inside 25 minutes.

His side were nevertheless progressive enough to finish with 18 shots, even if too few were accurate. Caoimhin Kelleher, standing in for the injured Alisson, was not unduly tested before he made a fine save from the substitute Luis Sinisterra. In a late flurry, Bournemouth hit the bar. And yet it was a postscript. The game had been decided by Diaz’s brilliance. Not for the first time, either.