Jürgen Klopp hurtled towards the Kop in celebration of Mohamed Salah’s magnificent 21st league goal of the season. His goalkeeping coach, John Achterberg, performed a forward roll on to the pitch, clipboard still in hand. It was the 91st minute at Anfield and Liverpool had taken a significant step towards Champions League qualification against Tottenham Hotspur. In the 95th, it was taken away.

Spurs departed with the point their second-half dominance merited but only because of a contentious penalty, their second of the game, after Virgil van Dijk was adjudged to have kicked Érik Lamela deep into stoppage time. Harry Kane had failed to convert from the spot 10 minutes earlier but made no mistake with his unexpected opportunity to make amends and claimed his 100th Premier League goal. “Big, big balls,” explained his manager, Mauricio Pochettino.

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Liverpool were incensed. Jon Moss had initially waved play on but was swayed by the insistence of his assistant, Edward Smart, that Van Dijk kicked Lamela on the back of the knee as one last ball dropped inside the Liverpool area. He did. Klopp claimed Lamela had deliberately backed in, looking for and maximising contact. He did.

Between the 85th and 95th minutes, two disputed penalties sandwiched a fabulous solo goal from Salah. An enthralling contest came to a dramatic and controversial climax and there was no disguising the happier manager on the final whistle. Pochettino punched the air while Liverpool players berated the officials, chants of “Cheat, cheat” rolling from the stands and Klopp raged at what might have been.

A five-point gap in the race for a top-four finish was returned to two with Kane’s spot kick, and controversy overshadowed a stunning contribution from Salah. Victor Wanyama, another Spurs replacement, injected his own touch of quality to cancel out the Egypt international’s early opener. Tottenham remain firmly in the hunt for a Champions League spot.

The game started and ended in a frenzy, of Liverpool’s and Smart’s making respectively. Klopp’s team swarmed forward from the off and did to Spurs what they had done to Manchester United in midweek in making a swift breakthrough. The goal was a personal milestone for Salah and a moment to forget for Eric Dier. In attempting to assist Kieran Trippier and Davinson Sánchez in clearing up Sadio Mané’s dangerous flick, Dier succeeded only in playing Salah clean through. Quickest to spot the possibility, Salah burst ahead of Sánchez and convincingly beat Hugo Lloris with a cool strike into the bottom corner.

Quick guide Ten minutes of Anfield madness Show Hide 84 mins Harry Kane, clearly in an offside position, is played through on goal by Dele Alli before being taken down by Liverpool’s under-fire keeper Loris Karius in front of the Kop. 87 mins Kane dusts himself down after being upended by Anfield’s No 1 but the keeper makes amends for his error by saving the England man’s poor penalty to leave it 1-1. 90+1 mins Somehow Liverpool’s player of the season Mohamed Salah wriggles free of the Tottenham defence and fires beyond Hugo Lloris to set Anfield alight. 90+3 mins Liverpool’s big-money signing Virgil van Dijk touches Erik Lamela in the box and, after lengthy consultation with his assistant, Jon Moss gives Spurs a second penalty. 90+5 mins Kane, after the long wait, keeps his cool this time around to silence the Kop and make it 2-2 to notch up his 100th Premier League goal and finish a breathless match. Photograph: Paul Ellis/AFP

The finish and the celebration that followed were those of a player who finds the Kop goal as a matter of routine. It was the Egypt international’s 20th Premier League goal of his debut campaign at Liverpool, arriving in his 25th game. No Liverpool player has reached that tally faster in the Premier League era – and they’ve had a few good ones.

Pochettino started with a midfield diamond of Mousa Dembélé at the base, Dier and Dele Alli right and left respectively and Christian Eriksen at the tip. It created and protected little in the first half but their improvement in the second half, when Eriksen shifted left and Alli advanced, was marked.

Liverpool could have established a more comfortable lead by then. The hosts posed the greater threat before the break only for a consistently poor final ball to undermine their efforts. At one stage Mané was unable to pick out Roberto Firmino having dispossessed Sánchez on the touchline. In the final seconds of the half Mané repeated the trick, found Salah and burst clear into the area but the return pass from the goalscorer was overhit, to Klopp’s obvious disgust. Firmino also sent a glancing header wide and Lloris saved from the commanding Van Dijk.

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Alli was instrumental in turning the game Tottenham’s way after the interval. The visitors dominated possession and territory, but were struggling to find a way past Loris Karius until Wanyama’s thunderbolt. Alli sent Son Heung-min clear with an exquisite flick but the Liverpool keeper stood tall and blocked the shot, the England international driving the rebound wide. Alli was then booked for simulation when he collapsed in the penalty area, looking for a Dejan Lovren tackle that never materialised.

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Tottenham’s attacking impetus increased with Pochettino’s bold introduction of Lamela for Sánchez, a central defender. His second substitution, bringing Wanyama on for Dembélé, had a immediate impact. With his first touch the midfielder found Eriksen in space on the left. With his second he found the top corner from 25 yards. Eriksen’s first-time cross was punched straight out by Karius. Emre Can failed to clear, Alex Oxlade-Chamberlain failed to react and Wanyama got there first to send an unstoppable finish beyond the Liverpool goalkeeper.

The drama had only just begun. Spurs were awarded a penalty with five minutes remaining when Kane rounded Karius and tumbled over the German stopper. The striker was offside when Alli released him inside the area but the ball deflected off Lovren and, after a lengthy consultation with his assistant, Moss stuck to his original decision. Liverpool thought justice done when Kane sent the spot-kick straight down the middle and Karius saved comfortably.

In the 91st minute Salah appeared to win the game for Liverpool with another moment of brilliance. From a throw-in on the right he somehow wriggled clear of Alli, Ben Davies and Jan Vertonghen before prodding over Lloris from close range. The Liverpool bench erupted in joy. Moments later it erupted in anger.