Daniel Sturridge and Roberto Firmino scored as Liverpool deservedly defeated eternal rivals Manchester United 2-0 in the first leg of their Europa League last 16 tie on Thursday.
Liverpool dominated the first ever European meeting between the teams from first minute to last, scoring through Sturridge's 20th-minute penalty and Firmino's 73rd-minute effort to put Jurgen Klopp's men firmly in the driving seat ahead of next week's return leg.
United would have lost much more heavily had it not been for the brilliance of goalkeeper David de Gea and failed to create a meaningful chance as manager Louis van Gaal's four-game winning run against Liverpool came to a juddering halt at a fervent Anfield.
"I think it was absolutely deserved," said Klopp.
"It was a great performance from first second to the last. It's only the first leg, but we needed to win it and we did it."
With both teams struggling to finish in the top four in the Premier League, victory in the Europa League looks their best hope of qualifying for next season's Champions League.
It is Liverpool who have one foot in the last eight and while United must gather themselves for Sunday's FA Cup quarter-final at home to high-flying West Ham United, Klopp has a full week to prepare his side for their trip to Old Trafford.
"I have to say that Liverpool created an atmosphere that was fantastic," said Van Gaal, who described both Liverpool's penalty and second goal as "cheap".
"They played very good in the first half and we could not cope with their pressure.
"It's difficult because 2-0 is a very difficult result for us. But we have to create an atmosphere like Liverpool's fans have done."
United breakthrough star Marcus Rashford started wide on the right and although he kneed the ball wide from an early Memphis Depay cross, he spent most of the first period deep in his own half tracking the forward runs of Liverpool left-back Alberto Moreno.
It was the same story on the opposite flank, where the recalled Nathaniel Clyne was keeping Depay on the back foot, and it was from their confrontation that the opening goal stemmed.
Depay was adjudged to have pulled Clyne back after getting caught the wrong side of the England full-back and Sturridge planted the ensuing penalty past De Gea.
With United's wingers pinned back and Firmino, Adam Lallana and Philippe Coutinho buzzing around behind Sturridge, the visitors found themselves under siege and De Gea had to come to their rescue three times before half-time.
Coutinho gave United a huge let-off when he used the outside of his right foot to prod a dribbly shot from Sturridge towards a vacant goal, allowing De Gea to claw the ball off the line in spectacular fashion.
The Spaniard then flew out to block from Sturridge, after Chris Smalling had misjudged a flighted pass from Firmino, before producing a stunning reflex stop to repel a Lallana volley from point-blank range.
Booked for a late challenge on Moreno shortly before half-time, Rashford came off at the interval and was replaced by Michael Carrick, who dropped into a back three as Van Gaal sought to stem Liverpool's first-half dominance.
It gave United a foothold in the game and they registered their first effort on target when Morgan Schneiderlin shot at Simon Mignolet from the edge of the box.
Depay also created a chance for Anthony Martial, only for the Frenchman — a peripheral figure throughout — to get the ball caught under his feet.
But De Gea had to remain alert at the other end and he dealt authoritatively with powerful efforts from first Coutinho and then Clyne, before Jordan Henderson hoisted a shot into the Kop from Lallana's lay-off.
The second goal that Liverpool richly merited duly arrived 17 minutes from time as Lallana teed up Firmino to stroke home left-footed after Carrick made a weak attempt to clear Henderson's cross.