Talking pointsHow Klopp's Reds made history with another dominant win over Man Utd
Mohamed Salah's brace, along with efforts from Luis Diaz and Sadio Mane, saw the Reds go top of the table for at least 24 hours.
Here are five talking points from the contest...
Another 'final' won
The second game of Liverpool's triple-header with fierce rivals went exactly to script.
Having beaten Manchester's other top-flight club three days earlier at Wembley, the Reds flew out of the blocks in this encounter and never really looked like ceding control.
The victory took Jürgen Klopp's men to the summit of the Premier League once again, and all eyes will now be on Man City's home duel with Brighton & Hove Albion on Wednesday evening.
The Merseyside derby is next on the agenda and then the first leg of a Champions League semi-final.
This is what we're all in it for.
Sublime Salah
The No.11 continued to deliver against Man United.
Hat-trick hero from the October meeting, Salah created the opening goal on Tuesday, before doubling the hosts' lead with a clinical finish after 22 minutes. He then wrapped up the points shortly before the end.
He became just the second player in Premier League history to score and assist in home and away games with United in a single season.
Also against this particular opposition, Salah has now netted nine goals in his last six appearances in all competitions.
His contributions saw him extend his lead in the Premier League Golden Boot race and move level with Trent Alexander-Arnold (12) in the division's assist rankings.
An impressive double
Liverpool completed a Premier League double over Man United for the first time since 2013-14.
They did so by putting nine goals past their arch-rivals this season – setting a new club record in the Premier League.
That figure eclipses the total of six Rafael Benitez's side recorded in the 2008-09 campaign.
And it equals the overall club record set in 1895-96. What a team.
A landmark Anfield goal
Diaz's opener after five minutes brought up goal No.400 at Anfield under Klopp in what was his 179th game in charge.
It was a typical, incisive move from the Reds, ending with Salah squaring for his forward partner to convert.
However, the second goal – No.401 – was even better.
Salah finished it off this time but was quick to show his appreciation for the incredible assist played by Mane.
Continuing to thrive in his central role, Mane sent the Egyptian through on goal with an instinctive, first-time flick that cut apart the United backline.
It was another piece of art this team seemingly produces on a weekly basis.
Putting things in perspective
What was rightly celebrated in May has already been secured in 2021-22.
Another set of three points added to Liverpool's tally has wrapped up a top-four finish and, therefore, Champions League qualification.
After it went down to the final day last season, Klopp's men have achieved the feat with six games to spare this term.
For further context on this squad's achievements, they eclipsed their 2020-21 points total (69) on April 2 with the win over Watford.
AcademyU18s match report: Comeback at Birmingham sends Liverpool to PL Cup quarter-finals
MatchThe opposition lowdown: Southampton
Interview'We can't take our foot off the gas' - Caoimhin Kelleher previews Southampton v Liverpool
Play nowCaoimhin Kelleher birthday quiz: Can you get 9/9?
FeatureClinical Harvey, Robbo's 'bullet' and Danns shock - things spotted in Friday's training