Matches like this are what the Premier League does best, fast-paced blockbusters with breathtaking attacking and thigh-slapping clangers. Leicester and, especially, Liverpool are among the leading exponents of an intoxicating genre.

Jürgen Klopp’s men scored three splendid goals here but still needed Simon Mignolet to save a late penalty from Jamie Vardy to secure a much-needed win. Mignolet, almost inevitably, had conceded the penalty himself, rushing off his line in an attempt to intercept the ball, which he touched before clattering into Vardy. The goalkeeper also bore some blame for earlier goals by Vardy and Shinji Okazaki, even if he was not helped on those occasions by questionable refereeing.

In the end, however, Liverpool banked three points because their vibrancy going forward more than offset their problems at the rear, earning reward in the form of goals by Mohamed Salah, Philippe Coutinho and Jordan Henderson.

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It would be wrong to claim the German came into this game with many Liverpool supporters calling for his head, but it is true that a lot were questioning what goes through it. In particular, the failure to shore up a persistently leaky defence remained a vexing puzzle. After losing here in the Carabao Cup on Tuesday Klopp had said he was sick of conceding preventable goals. He would have been well advised to pack anti-nausea tablets this time, even though he was able to deploy his preferred centre-backs with Dejan Lovren and Joël Matip having regained fitness.

That duo, along with several other Liverpool players, could do with silencing a growing number of sceptics. They also had to subdue Vardy and Okazaki, who set about testing them early on. In the fifth minute Okazaki released his strike partner, who sprinted past Matip and into the box. Mignolet blocked his shot at the near post and, with Lovren hesitant, Riyad Mahrez pounced on the rebound but whacked the bouncing ball over from seven yards.

Then Liverpool found their attacking groove. Coutinho and Salah, both thrumming dangerously, combined slickly to create their first chance, although Emre Can still had plenty to do. The German almost did it perfectly but his drive from 25 yards bounced off the base of a post. Salah swatted the rebound wide from close range but turned out to be offside.

Facebook Twitter Pinterest Simon Mignolet saves Jamie Vardy’s second-half penalty. Photograph: Laurence Griffiths/Getty Images

Salah was sharper three minutes later when he opened the scoring. The Egyptian sneaked behind Ben Chilwell to meet a lovely cross by Coutinho and send a powerful header into the net from an acute angle. Kasper Schmeichel seemed to be taken by surprise.

The same could be said of Mignolet moments later when the Belgian goalkeeper, as too often, was caught dozing. As he took his sweet time to kick clear outside his area, Vardy darted in to dispossess him. The ball squirted out to Okazaki, whose attempt to fire into the net from 25 yards was deflected wide.

As if reminded that they would probably need to score more than once to win, Liverpool hurtled quickly down the other end. Alberto Moreno was tripped outside the area and Coutinho curled a sumptuous free-kick into the net. The Brazilian was excellent throughout, showing why Barcelona covet him and Liverpool cherish the 25-year-old.

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Leicester halved the deficit before half-time, with Liverpool complaining of injustice. First Matip was booked when Vardy went to ground, then Mahrez swung over a corner, which Mignolet came for and missed after interference by Okazaki. Joe Gomez, jostled by Harry Maguire, was unable to prevent Wilfred Ndidi’s header from bouncing off him and towards the net. Okazaki nudged the ball over the line despite being pulled back by Mignolet.

There are managers who in such situations would shut the game down to complete a 2-1 away win. Klopp is no such manager, at least not with these players. He can tweak his approach but really has only one setting: frenetic. So the spectacle remained thrilling, the outcome unknowable. “We would have loved to control it but it was a little hectic,” said Klopp of the period just after half-time.

Leicester played their part well. The breakneck pace suited most of their players, too, but not Mahrez, who was mostly a drifter before being replaced by Demarai Gray. Matip blocked a shot by Vardy before, in the 68th minute, Liverpool broke fast to increase their lead. The substitute Daniel Sturridge unselfishly fed Henderson, who slotted past Schmeichel from the middle of the penalty area.

Still Liverpool were not safe. Leicester hit back one minute later, Mignolet parrying a shot by Gray into the path of Vardy, who accepted the invitation to score.

Two minutes later Mignolet conceded the penalty. Vardy blasted it down the middle and the goalkeeper stood up to it to ensure the last laugh was his, this time.