The Reds made the trip to a wet and windy south coast, knowing the victory would seal a place in the quarter-finals.
It was dominant opening 45 minutes from Jurgen Klopps side, who led through Cody Gakpos poached effort, but they didnt have things all their own way after the break.
Joe Gomez was forced to make a vital clearance on the line to prevent a goal and Justin Kluivert headed home an equaliser midway through the second half.
Substitute Nunez then curled home a stunning strike from an angle to put Liverpool back ahead, and they held on in horrible conditions.
These Liverpool fans took to social media to react to the Reds win.
Get in red men. Not the easiest conditions to deal with. Made up with that
Ian Ryan (@Ian1892T) November 1, 2023
Another step closer to that inevitable 0-0 after-extra-time domestic cup final with Chelsea. Up the Reds.
Ryan (@ryan3levis) November 1, 2023
We`re going all the way baby! domestic double, piece of cake!
nuneznunez in the This Is Anfield comments
That was grim weather but its another sign of Liverpool just getting jobs done. A proper team again. Oh, and Darwin Nuez is on fire.
George Reid (@reid1892) November 1, 2023
Well in, Reds. Hard-earned in horrible conditions.
We 100% lose that last season.
Henry Jackson (@HenryJackson87) November 1, 2023
Quansah been great tonight, serious composure.
Rory Greenfield (@RoryGreenfield) November 1, 2023
Jarell Quansah MOTM there. Outstanding. His emergence has been one of the main positives from this season so far. Top talent who looks more than good enough to be a Liverpool CB in the years to come.
Jack Sear (@JackSear) November 1, 2023
Quansah just keeps impressing. Mature and strong modern-day centreback. Good on the ball both in carrying and passing. A player who really deserves to get more and more chances. Giving him chances in the cups and some in PL this year could be perfect intro to Matips replacement.
Maxi (@MaaxiAngelo) November 1, 2023
Quansah was an absolute boss
Boldizsar Fejervari on Facebook
Quansah though, what a performance. Hell of a prospect.
Joel Rabinowitz (@joel_archie) November 1, 2023
Quansah has saved the club millions I reckon. Fantastic young talent
Ste Davies (@StevenD1977) November 1, 2023
Usually sceptical to praise young defenders given how many false dawns we’ve had in that position, but Quansah looks really, really solid. Held his own very well in all of his cameos and in a variety of different CB pairings. At the very worst he’s a great depth option.
barry (@BackseatsmanLFC) November 1, 2023
That finish is like a Batistuta in his prime! Where you just say fuck off as you smack it
Gym Guy (@A_GymGuy) November 1, 2023
Darwin is an agent of chaos and he is also a red ????
josh (@lfc_jdr) November 1, 2023
Nunez is the freakin Nuclear Option, isnt he?
Jack OLantern in the This Is Anfield comments
This is probably one match that Dom played and did not deserve the MOTM. Darwin this time.
Vlatko Georgievski in the This Is Anfield comments
Liverpool have won two matches by a one goal margin this season.
Nez with the winner at NewcastleNez with the winner at Bournemouth
Up the Reds.
Andrew Beasley (@BassTunedToRed) November 1, 2023
Stunning goal from Torres, I mean, Nunez.
Ben Webb (@BenWebbLFC) November 1, 2023