Palace 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 second and within three points of Liverpool at the top of the table.
Arsenal can move back into second and cut the gap on their title rivals to two points when they travel to Newcastle on Sunday.
Meanwhile, 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 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.”
In other games, Chelsea were also 3-1 losers, suffering a defeat on the road to Brighton while Tottenham managed to salvage a last-gasp 1-1 draw against Wolves.
Manchester City, meanwhile, continued to build on their improving form with an emphatic 5-1 win at home to Burnley. (AFP)
