Could things get any better for Crystal Palace? Now the only unbeaten side left in the Premier League having stretched their run to 18 matches thanks to this dramatic late victory over champions Liverpool, Palace are about to embark on their first European tour when they face Dinamo Kyiv in the Conference League on Thursday and have a manager that is proving to be a bit of a genius.

Arne Slot’s expensively assembled side thought they had kept up their run of rescuing late points when Federico Chiesa equalised Ismaïla Sarr’s opener. But the winning goal came from another substitute as Eddie Nketiah’s injury-time sent the home supporters wild as they recorded their first victory against Liverpool here since November 2014. But while Marc Guéhi put in another faultless performance against the club that came so close to signing him earlier the month, above all this was a triumph for the system that has been implemented by Oliver Glasner since he arrived in south London 18 months ago. On this form, Palace are a match for anyone.

A settled side has been one of the keys to their recent success and the return of Sarr from injury meant Glasner was able to name the same team that started the FA Cup final and Community Shield, apart from new signing Yeremy Pino replacing the departed Eberechi Eze. Liverpool still haven’t settled on their first choice XI after a busy summer of recruitment.

Having spent almost a combined £250m on Florian Wirtz and Alexander Isak, Slot probably felt compelled to start them both – especially after Hugo Ekitiké’s unhelpful red card in midweek ruled him out of contention. But Liverpool looked a far cry from the team that started this season with five straight wins as Palace seized the initiative in the first half. As well as possessing a rock solid defence, Glasner’s side have also become lethal from set-pieces under the Austrian – as Liverpool found to their cost in the ninth minute. Virgil van Dijk’s loose pass was intercepted by Tyrick Mitchell and after breaking upfield, Palace won a corner. The impressive Daichi Kamada’s inswinger was headed by Ryan Gravenberch under pressure from Guéhi and it fell perfectly for Sarr to sweep home. It should have been 2-0 in the next attack when Kamada pinched the ball off Gravenberch but Pino could not convert Sarr’s cutback.

Ismaïla Sarr fires Crystal Palace into an early lead. Photograph: Jonathan Brady/PA

Liverpool looked stunned and they had to wait almost five minutes to take a free-kick after a medical emergency in the crowd that required the intervention of medics. All was well in the end before Mohamed Salah hit the wall and a brilliant save from Dean Henderson somehow diverted Gravenberch’s piledriver on to the post. The direction of traffic was largely one way, however, and only two stunning saves from Alisson kept Liverpool in touch. First the Brazilian did well to scoop Daniel Muñoz’s effort off the line before he stood tall against Mateta in a one-on-one.

Ibrahima Konaté had endured a particularly testing afternoon having earlier been booked for hauling down Jean-Philippe Mateta but the France defender was inches away from equalising when he headed Dominik Szoboszlai’s corner wide. Palace’s dominance was underlined by the fact that Isak recorded only his sixth touch of the first half during 10 minutes of stoppage time that were added on. Another flowing move started by Maxence Lacroix’s stunning pass ended with Mateta striking the post with a curling effort before he blasted just over on the volley. Half-time couldn’t come soon enough for Liverpool and Palace left the field to a deserved standing ovation.

It was inevitable that Slot would make a change but it was perhaps surprising to see the ineffective Wirtz stay on. Instead, Conor Bradley was replaced by Cody Gakpo as Szoboszlai reverted to right back and the German moved into midfield. He seemed much more at home there than stuck out on the left flank, with Wirtz setting up Gakpo for a shot that wasn’t far away from Henderson’s post before forcing the Palace goalkeeper into a point-blank save from Szoboszlai’s cross that he really should have scored from.

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Isak was the next to spurn a big chance after wriggling his way into the penalty area before firing wide. “What a waste of money,” sang the Palace supporters. Chiesa thought he had earned Liverpool a share of the spoils when he capitalised on a mistake from Chris Richards to slam home the equaliser. But this was an afternoon too savour for Palace as Nketiah provided the killer blow after the visitors failed to clear a free-kick deep into stoppage time.