Mohamed Salah scores hat-trick in 5-0 win at Old Trafford registering Liverpool's largest success against United since 1925. Separately, Real Madrid beat Barcelona 2-1 at the first football match since Ramos and Messi's departure.
Liverpool have inflicted a historic hammering on Manchester United as Mohamed Salah scored a hat-trick in a 5-0 win at Old Trafford, leaving Ole Gunnar Solskjaer clinging to his job.
For the first time in Premier League history, United trailed 4-0 at half-time and failed to score in a hopelessly one-sided contest on Sunday. The Red Devils have now taken a run of one point from a possible 12 in the league.
Naby Keita started the rout before Diogo Jota doubled Liverpool's lead inside 15 minutes.
Salah then took centre stage to take his tally for the season to 15 goals in 12 appearances and become the top-scoring African player in Premier League history in the process.
To round off a miserable day for United, Paul Pogba lasted less than 15 minutes as a second-half substitute as he was shown a straight red card for a reckless lunge that forced Keita to leave the pitch on a stretcher.
Liverpool's first victory in front of a crowd at Old Trafford under Jurgen Klopp moves them back above Manchester City into second, just a point behind leaders Chelsea.
By contrast, United's hopes of a first league title since 2013 already look over as they remain eight points off the leaders.
That gap is likely to grow in the coming weeks with Tottenham and City to come in the next fortnight before an international break.
Whether Solskjaer will still be in charge come November is now in serious doubt as he has completely failed to form a balanced team from a talented collection of star players.
The Norwegian will wonder what might have been had Bruno Fernandes not fired over a glorious chance to open the scoring on three minutes.
But soon the defensive cracks that have blighted United's season began to appear.
Salah teed up Keita to open the floodgates after just five minutes with a composed low finish past David de Gea.
Ronaldo avoids red card
United came from 2-0 down at the break to beat Atalanta 3-2 in the Champions League on Wednesday.
But former midfielder Paul Scholes' warning after that match that Liverpool would be 4-0 up in 45 minutes if handed the same space to attack into came to fruition.
Jota justified his selection ahead of Sadio Mane as he stretched to turn in Trent Alexander-Arnold's cross to double Liverpool's advantage.
Salah has now scored in 10 consecutive games and overtook Didier Drogba with his 105th Premier League goal when the Egyptian turned home Keita's cut-back with the United defence all at sea.
Cristiano Ronaldo was lucky to avoid a red card as United's frustrations bubbled over in first-half stoppage time when he was booked for lashing out at Curtis Jones in a sign of what was to come as the home side lost their discipline.
Liverpool inflicted further punishment before the break when Salah smashed home his 14th goal in 12 games this season at De Gea's near post.
Salah then completed his hat-trick with another cool finish five minutes into the second-half after Jordan Henderson's pass dissected the United defence once more.
Ronaldo thought he had pulled a goal back only for a VAR review to catch him in an offside position.
Another VAR check saw the end of Pogba's brief cameo for a horrendous studs-up challenge on Keita that forced the Guinean off.
Solskjaer sacrificed Fernandes and Marcus Rashford to try and stop the bleeding as Old Trafford emptied during the final half hour.
De Gea ensured Liverpool failed to match their record margin of victory against United with an incredible save from Alexander- Arnold's drive.
However, that did not subdue the mood among the travelling fans as they mockingly chanted for Solskjaer to remain in his job.
Real Madrid beat Barcelona to win El Clasico
Meanwhile, in another high-voltage game, Real Madrid beat Barcelona 2-1, the first match between the rival clubs since the departure of Sergio Ramos and Lionel Messi.
Argentine star Messi was with Barcelona, while Spanish defender Ramos played for Real Madrid since 2005 until they both transferred to PSG this summer.
The match started without many thrills, but Real Madrid's Austrian defender David Alaba opened the score in the 32nd minute at Camp Nou.
Both sides played an evenly matched game, and no goals were scored until the 90th minute.
Lucas Vasquez scored a late second goal in the 94th minute and made it 2-0 for Los Merengues.
Just before the end, Sergio Aguero, who entered the game late, scored the only goal for Barcelona in the 97th minute and Real Madrid won 2-1 in the La Liga week 10 game.
With this victory, Los Merengues have defeated Barca four times in a row in official matches, an achievement which they haven't been able to pull off since 1965.
Real Madrid currently sit on top of the La Liga table with 20 points, while Barcelona are placed 8th with 15 points.