Liverpool marched on, though with no little relief, their post-match celebrations reflecting the importance of victory. Arne Slot’s team had not triggered the traps Andoni Iraola’s Bournemouth had used to snare the top-four contenders Manchester City, Arsenal and Nottingham Forest this season.

It was Mohamed Salah who snatched the three points. If his first came after a highly debatable penalty award, the second, a left-foot chip like a prime Tiger Woods approach shot, was a goal of inarguable beauty. In negotiating one of their most demanding remaining assignments, Slot’s team, now nine points clear, sent the pressure back into Arsenal’s fraying mindset. Salah’s goals are guiding Liverpool to their key objective. “My main target is to win the Premier League with the team, we are going in the right direction,” said the Egyptian king.

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A game too far for Bournemouth? Where Liverpool fielded the same XI that swept aside Ipswich last week, their near fully-fit squad offered options. Curtis Jones’s second-half arrival brought energy and improvement when necessity demanded Iraola’s starting selection was again down to the players he has available.

“Small things didn’t go for us,” said the Basque. “We have given ourselves a chance, but it hasn’t been enough.”

Slot said: “We had to play on top of our abilities and we needed a bit of luck to win this game. They were constantly trying to do things. I didn’t think we controlled the game.”

His team kept on their sure-footed path when the Vitality Stadium had previously staged a couple of slips for Jürgen Klopp, a 4-3 December 2016 comeback under Eddie Howe and, under Gary O’Neil two seasons ago, when Salah missed a penalty.

Bournemouth’s rise, via dazzling speed and movement, has made opponents question their own existence. Last week’s signature destruction of Forest had been rendered even more extraordinary by Saturday’s earlier events at the City Ground. And yet Liverpool escaped such a fate despite Bournemouth going for their throats.

That Trent Alexander-Arnold’s flank was targeted was clear, Justin Kluivert often joining in on the overload. Antoine Semenyo, cutting in, smashed the post after sending Alexander-Arnold to a different postcode – Pokesdown, Southbourne? – with a drag-back. Liverpool had made one of their more circumspect starts, with only a couple of flickers, Cody Gakpo zipping in a shot, Salah having a similar, low effort into the arms of Kepa Arrizabalaga.

Liverpool’s lead came via controversy. Darren England’s decision that Lewis Cook had clipped Gakpo’s heels looked soft, softer yet on the replay, but VAR went with the referee’s call. This time, Salah slotted his penalty for a 20th Premier League goal of the season. That flashpoint turned the home crowd rancorously against the officials, and blew much wind from their team’s sails. Further disappointment arrived when David Brooks had the ball in the net only for Milos Kerkez’s blindside run to be ruled offside by a long-delayed VAR call.

Where previously Bournemouth have been incisive, clear-thinking in decision-making, Iraola’s team became guilty of overplaying, though Liverpool’s calm, ordered defending, marshalled by the talkative though rarely fazed Virgil van Dijk, deserved due credit.

Beyond the break, Bournemouth attempted to resume normal service and blazed into their opponents. That forced Liverpool into their period of most discomfort. Kluivert swung at a volley that was beaten away, and Ryan Christie’s toe-end pass put Semenyo in on Alisson, the goalkeeper only just smothering the danger. “You have to be focused and really sharp in every situation,” said the Brazilian. “This intensity takes a lot of energy to win these games.”

Bournemouth’s risk-taking led to space opening up. Salah dragged wide as Dominik Szoboszlai and Alexis Mac Allister became increasingly prominent. When Alexander-Arnold departed with an injury Slot reorganised his team, demonstrative but without histrionics, before more danger was ridden out. Marcus Tavernier, on as a sub, cracked a post from 25 yards and Kluivert missed the rebound. “At the end, against teams like Liverpool, you need to punish them whenever you have the chance,” said Iraola.

Within moments, Salah had struck again. “Maybe that second goal was the difference between the two teams,” said Slot. Any further danger was shut down as Wataru Endo, who these days resembles a baseball closer, came on to compress midfield and see out an important win over a highly dangerous opponent.