The biggest win in the history of the league was equalled by the Reds when they thrashed Bournemouth at home.
After two draws and a loss to Manchester United, the Reds responded in stunning fashion, despite the manager describing the start to the season as a false start.
In 1995 and last year, Manchester United andLeicester City achieved this margin of victory against their opponents.
Two goals in the first five minutes against the Cherries gave the Reds a great start at home.
LuisDiaz rose to powerfully head home and the impressive HarveyElliott curled in his first top-flight goal with a wonderful strike from outside the box
Trent Alexander-Arnold hit a long-range shot into the top corner with the help of Roberto Firmino.
The Brazil forward scored from inside the six-yard box on the half-hour mark and then headed in the fifth from a corner before the break.
In the first minute of the second half, Chris Mepham diverted the ball into his own net and Firmino was on hand to score.
With eight minutes left in the game, Carvalho volleyed in for number eight and in the ninth, Diaz headed in for the win.
Bournemouth have lost their last three league games without scoring a goal after beating Villa in their opener.
After failing to win any of their first three games, it had been suggested that the team looked sluggish.
Questions were raised about the title credentials of a Reds side that ended last season on two low points after a sluggish showing in a loss to Manchester United.
An extensive injury list - notably in the middle - and a big summer signing has not helped, and as a result, the visitors had no response.
The Reds had a total of 19 shots at goal and 12 of them were on target.
They had not racked up that number since 1989 when they did against Crystal Palace.
After giving up the first goal in their last seven games, the Reds were on their way after just two minutes with a well- timed headed goal.
After the side's slow start to the season, the goal will have given the crowd some relief.
The teenager opened his league account for the Reds with a wonderful curling effort into the bottom corner before Alexander-Arnold slammed into the corner from outside the box.
Firmino ended a run of 20 league games without a goal with an opportunist strike, while Van Dijk shrugged off a difficult game at Manchester United to head in the fifth.
Chris Mepham's own goal, Firmino's second and Carvalho's first for the club made it a perfect afternoon for the Reds as they narrowly missed out on their biggest victory of the season.
In a game in which their team-mates were ruthless, it should have been double figures for the Reds.
The Egypt forward missed an open net from a couple of yards out, then had a shot tipped over by Mark Travers, and Andrew Robertson headed over.
In the 34 meetings against teams that have been promoted from the Championship, the Reds have lost just one of them.
It has proved to be a false dawn for Bournemouth since they returned to the top flight and the rest of August has been miserable.
The south coast side was thrashed by Manchester City, lost at home toArsenal and then capitulated after giving up two goals in the first five minutes of the game.
The men have conceded more goals in the top flight this season than any other team.
Their total of 21 shots from their first four games is the second lowest in the last five years.
Alisson was stretched all game, but he was the one who was stretched the most in the afternoon when he plucked a weak Kieffer Moore headed out of the air.