The bad news for Harry Kane is that Mohamed Salah is not standing still waiting to be caught. The Liverpool forward became the first player to reach 30 league goals with a delightful second-half header, leaving him one goal short of the record for a 38-match season, with four games to play.

In all competitions Salah has 40 for the season, enough to join the ranks of Liverpool royalty. Only Roger Hunt and Ian Rush have managed that feat before. One more league goal and Salah joins Alan Shearer, Cristiano Ronaldo and Luis Suárez as joint top scorers for a 38-game Premier League season, although the chances are he will go out in front. He may even reach or pass the 34 goals Shearer scored in the original 42-fixture Premier League, though for the moment Liverpool are sufficiently impressed with the Rush connection.

“Thirty-one years since Ian Rush scored 40?” Jürgen Klopp asked in mock disbelief. “He doesn’t look that old. Was he 14 years old at the time? Mo knows the way we play suits him. Perhaps the boys were searching for him a bit too much, but it is a win-win situation. He wants us to be successful and we would love him to get the Golden Boot.”

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Salah had already had a couple of chances by the time Liverpool took the lead on seven minutes. Jordan Henderson sent a diagonal cross into the box and though Asmir Begovic kept out Sadio Mané’s initial header from close to the penalty spot he could not keep hold of the ball, and the Senegal forward lost no time in tucking away the rebound.

Though Jordon Ibe did try to hit back against his former club with a speculative drive that flew a couple of feet over Loris Karius’s crossbar, once Liverpool had taken such an early lead there was more interest in whether or not Salah would get on to the scoresheet than the outcome of the game.

Apparently piqued by Kane’s nerve in bulking up his total with a disputed goal, Salah made it clear from the outset he was keen to find the target. He brought a save from Begovic midway through the first half when it might have been more rewarding to pass to a colleague than shoot, and when a stray Simon Francis pass gave him a chance to run at the Bournemouth defence a few moments later he again showed little inclination to part with the ball, even though he must have known he had a slim chance of scoring with a rising shot from the edge of the area.

The second half began in a fashion that was actually quite tedious. The fact that Liverpool only had one attacking effort of note for a quarter of an hour might give some indication of how tedious. Roberto Firmino ran offside on a couple of occasions but that was about it for excitement. A 50-yard break by Trent Alexander-Arnold did bring Salah back into the game just after the hour mark, though by his standards the eventual shot was tame and straight at the goalkeeper.

The danger with just one goal separating the teams was that Bournemouth might sneak back into the game and share the points with a single effective attack, yet at the mid-point of the second half a couple of Salah-related incidents brought the stadium to life.

First he went flying in the penalty area claiming a push in the back from Nathan Aké. It was in some ways similar to the Juventus foul Michael Oliver did so well to spot in midweek, though Chris Kavanagh was having none of it and replays proved him right. Aké did raise his hands, unwisely, and Salah may have felt the contact, though there was not even a hint of a shove.

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Less than a minute later Salah had his revenge, drifting in behind Aké to get his head to Alexander-Anold’s cross and put Liverpool two in front. That barely does his 30th league goal of the season justice, for Salah still had to apply the right amount of power and precision to get the ball above and beyond a 6ft 5in goalkeeper. In effect he lobbed Begovic while facing away from goal, showing the sort of instinctive finishing that has become his trademark. He made a difficult chance look easy. No wonder Kane is worried.

Karius had to make a stop from Dan Gosling after that but Liverpool were never seriously threatened. Firmino could have made it 3-0 a few minutes before he scored, though after missing one good chance through over-elaborating in front of the Kop he made sure he buried his next one.

“Liverpool have really improved in the last year,” Eddie Howe said, when reminded his team took a point from Anfield last season. “They are tough to play against at the moment.”