Then came the most dramatic ending imaginable.
The game seemed to head for a draw before Origi, brought on in the 84 minute, nodded in from close range after the ball hit the cross bar and bounced back.
Divock Origi was the unlikely hero at Anfield as he scored from inches out in the 96th minute to ensure the gap between Liverpool and Premier League leaders Manchester City remains at two points. "I'm not sure what he was trying but he forced the 'keeper to make an error", he said.
One of the most controversial moments of the game was Jürgen Klopp's over-exuberant celebration of Origi's victor when he ran onto the pitch to celebrate the goal with Becker.
Liverpool's goalkeeper, Alisson, was one of those who went up to Pickford and he showed his class by giving him a hug and having a few words in his ear.
Everton goalkeeper Jordan Pickford during the Premier League match at Anfield
We're still not even at the halfway stage of the season, but with City showing signs of invincibility at the top of the table, any failure by Liverpool to beat their neighbours at Anfield on Sunday would have given the champions at least a four-point cushion - five, if Everton had won at Anfield for the first time since 1999.
"I'm sure there'll be a few exhausted bodies but it's well deserved and it's all worth it when you go home and you're sitting with your family with three points in the bag". He has rarely played for Liverpool since. Dier celebrated his equalizer by making a shush gesture in front of Arsenal fans and it prompted a scuffle between both sets of players, with substitutes also getting involved in the squabble.
Alexandre Lacazette came off the bench to put Arsenal ahead and Lucas Torreira sealed the points with his first goal for the club. "Last season sometimes with a two and sometimes with three, but in a central position, so it's normal that he needs to improve".
It was a cruel way to end a polished display from the travelling Toffees.
It was typical scavenging work by Kante, who was called out publicly in midweek by his coach Maurizio Sarri for his poor performance in Chelsea's 3-1 loss to Tottenham last weekend. "That's why it's the best game in the world!"
A lovely run down the right from Salah ended up in a cross-field pass to Roberto Firmino, who turned to get a shot away but it went wide before the 20th minute mark.