The second half saw plenty of pressure from the visitors, but Arsenal stood firm and doubled their advantage.
Salomon Rondon pulled one back in the 65th minute before Ayoze Perez's double earned the Magpies a third win from four games.
The inauguration in the first week of April also means that Tottenham will welcome the Champions League to their new ground in April. The striker combined beautifully with the returning Dele Alli for his 200th career goal and seventh in five games against shell-shocked Saints.
England captain Kane is their top scorer this season with 24 goals and his strike in Saturday's loss at Southampton was the 200th of the 25-year-old's club and worldwide career.
It now leaves Tottenham contemplating their chances in the top four and United, Arsenal and Chelsea are hot on their heels.
But someone was - Valery, who struck from close range to secure his second goal in two games following his stunning strike against Manchester United last week.
James Ward-Prowse free-kick caps Saints comeback against Tottenham
Yan Valery struck his second goal in two games in the 76th minute before James Ward-Prowse scored a stunning victor from a free-kick.
Everton raced to an early lead through Dominic Calvert-Lewin and Richarlison.
A penalty was awarded, but the England number one was not sent-off and then saved Matt Ritchie's resulting spot-kick.
"I am a little bit in shock because I think it's completely unfair", he said.
The fan, a Sunday Times journalist who has remained anonymous for fear of reproach, alleges hearing two men near him singing anti-Semitic songs during the first half of the game.
The damage was done by Junior Hoilett followed by Victor Camarasa on either spell of the half as the Bluebirds move off the bottom-three.
"That's what the crowd felt in the second half, that there's a team on the pitch fighting for every point and that was a moment to celebrate with them but also to tell them that it's only one step, a big one maybe".
However, Knockaert sparked wild celebrations from the Brighton fans when he curled into the top corner the victor 16 minutes from time.