He said: "I'm ecstatic and really proud - I feel privileged to have the support and the trust the club has in me to offer me a new deal". Palace has 22 points at 6-4-12 and sits four points clear of relegation.
But now, with the Englishman back on the Melwood training pitches under the careful supervision of Liverpool physios, he is nearing a return to full team training in late February or early March. Roberto Firmino and Sadio Mane have both scored eight goals, while Xherdan Shaqiri has scored six goals. They found an organised Brighton side hard to break down.
Alexander-Arnold's impressive performances over the last couple of seasons have seen him become Klopp's first choice at right-back, with Nathaniel Clyne having been loaned to Bournemouth as he struggled for game time.
Klopp's quadruple fist-pump in front of the Kop at the end showed just how tense - and how vital a result - it was for Liverpool.
A cagey first half concluded with a controversial penalty being awarded to Klopp's men when Mamadou Sakho was adjudged to have tripped Mohamed Salah inside the box; James Milner, as expected, converted the spot-kick to give Liverpool a slight advantage heading into the interval. We knew for different reasons the game would be hard. It was the Egyptian's 50th Premier League goal; only Andy Cole, Alan Shearer and Ruud Van Nistelrooy have reached that landmark in fewer games.
And Klopp believes his defender merits a chant from the Reds faithful.
I remember when we signed him back in the summer of 2017, I spoke a lot about "his story, his journey" and how much I loved it and thought it pointed to the type of person and player he would be for us.
What happened last time the two sides met?
Matip was an unused substitute against Brighton but he won't be rushed into action by Klopp after recovering from a broken collarbone. However, that can't be done with Liverpool as they were in a very similar position 5 years ago, and yet failed to clinch the title.
The Reds, who recalled James Milner, Joel Matip and Naby Keita, dominated possession but after missing a string of headed chances, Roy Hodgson's side made them pay when Andros Townsend finished off a slick move.
They did it the hard way this time around, but they can put their feet up now.