There is a relentlessness about this title race that is impossible not to admire. Liverpool, playing catch-up after Manchester City’s victory 24 hours earlier, once again did everything that was asked of them to regain top spot and leave their rivals with no margin for error in Wednesday’s derby at Old Trafford.

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The pressure was there for all to see and so was the relief on a day when Liverpool had to stay patient, hold their nerve and find a way to win a game that had frustrated them for the best part of an hour. In the end they came up with the answer themselves during a half-time conversation in the dressing room that led to the clever set-piece routine that broke Cardiff’s resistance.

Georginio Wijnaldum’s unerring first-time shot, from Trent Alexander-Arnold’s short corner, caught Cardiff out and any hopes Neil Warnock had of salvaging something from the game were extinguished nine minutes from time when Sean Morrison wrestled with Mohamed Salah and James Milner converted from the spot.

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Salah may have fallen a little theatrically – “I think the end of it was a 9.9 Tom Daley job,” said Warnock – but Morrison had his arms all over the striker in full view of Martin Atkinson, the referee. Although Salah looked a little disappointed not to have the chance to take the penalty himself, it was smiles all round come the end as Liverpool chalked up their ninth successive victory in all competitions.

Liverpool are up to 88 points, which is a Premier League club record and says everything about the standard Jürgen Klopp and his players have set this season. The bottom line, though, is that it will all feel rather hollow unless the campaign finishes with a first league title for 29 years.

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Liverpool are doing their bit on that front but the worry is that they need a favour from a Manchester United side in freefall. Klopp is focused only on Liverpool winning matches. “The points total is like a bill, you don’t know what it’s going to be, but when it comes, you pay it,” he said. “In the end we will see how many points we have and then we get what we get. If you are only motivated to win the holy grail, then something is wrong with you. We are motivated to play for this club, we want to win games because we enjoy the ride with the fans. But we have no influence on the other games.”

Liverpool were not at their fluent best, in particular their famed front three, who squandered some excellent chances, yet it was still a thoroughly professional team performance. Naby Keïta was an industrious presence in the centre of the pitch, Joël Matip strode out from the back with the ball on several occasions and Wijnaldum produced a splendid finish when Liverpool needed it most.

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From Cardiff’s point of view, this game had always felt like a free hit in their battle to avoid relegation, and there were plenty of positives to take, especially the performance of Nathaniel Mendez-Laing. Signed on a free transfer from Rochdale two years ago, his direct, penetrative running on the left flank caused Alexander-Arnold problems time and again in a first half that nearly ended with Cardiff taking the lead. Oumar Niasse’s acrobatic volley was superbly tipped over the bar by Alisson in the 44th minute.

Liverpool had wasted a few chances of their own by that point, with Roberto Firmino profligately shooting over and Salah’s stabbed effort blocked by Neil Etheridge’s outstretched boot.

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Wijnaldum was not so forgiving in the second half. As Alexander-Arnold shaped up to take a corner from the right, the Cardiff defenders expected the ball to be delivered into the six-yard box but the Liverpool full-back expertly disguised his intentions. His whipped, low centre picked out Wijnaldum in space and it was a terrific shot from 12 yards that flashed past Etheridge.

Warnock felt Cardiff should have had a penalty moments later, claiming that Andrew Robertson had hold of Morrison as the central defender tried to get on the end of a corner. Klopp claimed that Atkinson had told him afterwards he would have given Liverpool a free-kick for a foul on Alisson had the ball ended up in the back of the net.

Jordan Henderson should have given Liverpool some breathing space but wastefully fired Sadio Mané’s intelligent cut-back over the bar. Liverpool then lost Fabinho to concussion only moments after the Brazilian had come on but Milner, his replacement, quickly made Klopp feel at ease with his penalty kick. Only Etheridge’s fingertips prevented Salah from adding a third Liverpool goal.

“We wanted to give them a game, attack and not just sit back,” said Warnock, whose team will need a minimum of four points from their remaining three games to have any chance of staying up. “Whenever we could, we had a go at them. But they’re a good side, aren’t they? There’s not a weakness in their team.”