The Eagles are now the only undefeated team in the Premier League after extending their club record run to 18 games in all competitions without losing, including three games against Liverpool.
“These are the moments why we love football. The fans will have a great Saturday evening now,” said Palace boss Oliver Glasner.
“We deserved it. Great performance, great game, great win.”
The English champions were finally made to pay for another disjointed performance after being bailed out by a series of late goals in winning their opening five league games.
Ismaila Sarr fired the FA Cup winners into an early lead after Liverpool failed to deal with a corner.
Liverpool looked set to be rescued by another late goal when Federico Chiesa swept home a loose ball in the box to equalise on 87 minutes.
This time the Reds were on the other end of a late winner.
Nketiah produced a composed finish in a packed penalty area with almost the last kick of the game.
Victory takes Palace up to third and within three points of Liverpool at the top of the table.
Arsenal produced a dramatic late fightback to win 2-1 at Newcastle yesterday to move into second place in the table, two points behind Liverpool.
The Gunners were heading for a fourth consecutive defeat at St. James’ Park after falling behind to Nick Woltemade’s first-half header.
However, Mikel Merino headed in the equaliser before Gabriel Magalhaes powered in the winner from a 96th minute corner.
“To win in the manner that we have done it, wow, what a feeling!” Arsenal boss Mikel Arteta said.
“Football is about emotion and going through things and today we had a beautiful one at the end of the match.”
In yesterday’s early match, Aston Villa earned their first win of the season thanks to a 3-1 triumph over Fulham at Villa Park, with striker Ollie Watkins scoring his first goal of the season in the league.
Brentford bully Man Utd
United boss Ruben Amorim’s wait for back-to-back Premier League wins goes on, nearly a year into his reign, after a disastrous defensive display at Brentford.
Igor Thiago took advantage of mistakes from Harry Maguire and goalkeeper Altay Bayindir to put Brentford 2-0 up inside 20 minutes.
Benjamin Sesko’s first United goal was the only positive note for Amorim’s men as the Slovenian fired in at the third attempt before half-time.
The course of the game could have been very different had Bruno Fernandes not failed to score from the penalty spot for the second time already this season.
Fernandes’ spot-kick was saved by Caoimhin Kelleher after Nathan Collins was lucky to avoid a red card for pulling down Bryan Mbeumo.
Instead it was Brentford who sealed victory in stoppage time through Mathias Jensen, whose shot proved too powerful for Bayindir.
“We didn’t control the game. We played the game of Brentford,” Amorim said.
“All the crucial moments were against us. We need to do better.”
Manchester City needed some help from Burnley defender Maxime Esteve, who scored two own goals, in a 5-1 win for Pep Guardiola’s men.
Esteve turned into his own net under pressure from Phil Foden after Jeremy Doku’s effort was saved.
Against the run of play, Burnley hit back through Jadon Anthony to level before half-time.
City were growing frustrated until Matheus Nunes blasted in from Erling Haaland’s knockdown.
The unfortunate Esteve turned in Nunes’ cross to make it 3-1.
Haaland then struck twice in added time to take his tally for the season to 15 goals in nine games for club and country.
Chelsea beaten by Brighton
For the second consecutive weekend, Chelsea were undone by a red card in a 3-1 defeat to Brighton.
The Blues deservedly led at half-time through Enzo Fernandez’s header.
However, the game changed when Trevoh Chalobah was sent-off on 53 minutes after a VAR review for chopping down Diego Gomez who was racing clear on goal.
Brighton made the man advantage count as Danny Welbeck headed in to level before Maxim De Cuyper and Welbeck secured victory in stoppage time.
Tottenham needed a 94th minute equaliser from Joao Palhinha to rescue a 1-1 draw at home to bottom-of-the-table Wolves.
Newly-promoted Sunderland are up to fourth after Omar Alderete scored the only goal at the City Ground to leave Ange Postecoglou still without a win as Nottingham Forest manager.
There was also late drama at Elland Road where Bournemouth snatched a point against Leeds thanks to Eli Kroupi’s strike in a 2-2 draw.