Origi, who spent last season on loan in Germany at Bundesliga side Wolfsburg, was denied by the crossbar two minutes from time, before he scored his first Liverpool goal since May 2017 to inflict a fifth 90th-minute defeat on Everton in Merseyside derby clashes.
England and Everton goalkepeer Jordan Pickford's costly blunder allowed out-of-favour Divock Origi to carve his own piece of Merseyside history with a Liverpool victor deep into added time at Anfield.
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.
And the Liverpool manager accepted he overstepped the mark in a post-match interview with BBC Sport.
Klopp appreciated what he did might not have displayed the most grace and apologised after the game. "I apologised immediately after to Marco Silva, I didn't want to be disrespectful".
Everton - winless at their rivals' ground since 1999 - had a gilt-edged chance to take the lead in the fourth minute when Yerry Mina, incorrectly not flagged for offside, somehow headed Lucas Digne's free-kick wide with the goal at his mercy. "A lot of teams saw that we were good at that [Liverpool's counter-pressing style] and realised they were overplaying". I thought we were really unlucky not to get a point and could even have won it, if only for a goal line clearance and a freaky goal. We have always had a bit of class as a football club, their manager at the end, showed us all that he & his club know fuck all of the word "class". It was a long and open game. "I think it is the Everton luck when we come to Anfield", said Pickford.
"Not often, it happens from time to time but not very often", he added.
Arsenal's Pierre Emerick Aubameyang celebrates his goal in the 4-2 win over Tottenham Hotspur at the Emirates Stadium in London
As early as it is, being four points behind one of the best teams ever seen in the Premier League era would feel like an unbridgeable gap, even though Liverpool have conceded just five goals in the league all season.
Peep! We are underway in the Merseyside Derby! .
"Everyone is devastated and silent", said Keane. All the support I can give to Jordan [Pickford] I will.
"Everyone is devastated because of the work we put in".
Chance! Mane smashes it over the bar from close range! . We are devastated for ourselves and the fans.
Everton made six new signings in the summer, as well as appointing a new manager in Marco Silva, and the freshness was evident against Liverpool until the late, cruel victor conceded by the home side.
"We tried to control the game they had good counter-attacks".
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The team wraps up a four-game western trip Saturday in Sacramento after falling to the Los Angeles Lakers last night. But I'm available anytime we need a play to be made. "The success we had previous year , it wasn't just me.