Mohamed Salah scored twice as Liverpool beat Southampton 4-0 to go 22 points clear at the top of the Premier League with their 20th straight home league victory.
Moments after a strong appeal for a Southampton penalty was rejected, Jurgen Klopp's side took a hugely controversial lead through Alex Oxlade-Chamberlain's low shot just after half-time.
The league leaders then doubled their advantage on the hour through Jordan Henderson's close-range effort.
Henderson then teed up Salah to chip after Alisson's precise long pass, before Roberto Firmino's unselfish assist set up the Egypt forward for his second at the end.
The result puts Liverpool 22 points clear with second-placed Manchester City playing Tottenham on Sunday, live on Sky Sports Premier League, and the 20th straight home league victory equals the record set by City.
After the match, Saints boss Ralph Hasenhuttl bemoaned the decision leading to the opening goal.
He said: "You need brave decisions from the referee. To say 'no goal and penalty', here at Anfield, that won't happen.
"In the first half there was a backpass to the Liverpool goalkeeper [not given], that's another decision, maybe this is why it's so difficult to win here.
"It is a clear penalty."
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How Liverpool went 42 games unbeaten in the league
Southampton looked solid from the beginning, pressing high up the pitch, and restricted Liverpool to long shots and hopeful crosses early on.
After half an hour, Salah's pinpoint chipped through ball found a marauding Virgil van Dijk bursting through, but despite a lovely touch to control, his cheeky back-heel was blocked by Alex McCarthy and Firmino's follow-up snuffed out too.
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Before Southampton could get it clear, Henderson sent over a teasing looped cross from the right and Firmino tangled with Shane Long in the box, but the Irishman's light contact was judged insufficient to award a penalty after a VAR check.
The visitors - who took 10 shots at Liverpool in the first half, the most at Anfield since Chelsea in 2014 - threatened constantly and almost took the lead themselves. After Firmino's misplaced backwards pass, Danny Ings raced onto it, turned past Joe Gomez and struck it low and goalbound before being inadvertently blocked by Long's heels.
But Liverpool had their opener just after the break. As Ings drove into the box, he was seemingly caught by Fabinho, but play continued. After fine interplay between Andy Robertson and Firmino, Oxlade-Chamberlain drilled low into the bottom-left corner from outside the area for his second goal in two games.
After a slick, quick, passing move, Firmino played Salah through nicely but after he slipped the ball home past McCarthy, it was correctly ruled out for offside by VAR.
Henderson doubled the lead on the hour with a composed finish after Firmino's cute cutback and then turned provider after Alisson's precise long pass, feeding Salah who chipped confidently past McCarthy.
The Egyptian then had his second goal in added time when Firmino - instrumental throughout - squared unselfishly to Salah, who poked the ball in via a deflection off McCarthy despite Jan Bednarek's best efforts.
Liverpool's 22-point lead is the biggest at the end of a day in English top-flight history, also marking the longest winning streak on home soil since Bill Shankly's Liverpool side in 1972.
What the managers said
Southampton boss Ralph Hasenhuttl: "I would like to watch this game if we went one goal up. For 50 minutes the best team in the world had no real chances and we had a massive one.
"The way we played was unbelievably good and I am proud and stand by our plan.
"In the end it was a deserved win for Liverpool, but we played the best we can so I am very proud."
Liverpool manager Jurgen Klopp: "The readiness to improve and learn from the game is what we had to do to win. The set-up of Southampton I could not give more credit to.
"They had too many shots on target and we had to change in the second half. That helped massively and when we are rolling it's difficult to stop. Even when it was 4-0 Southampton did not stop and I have so much respect for that."
Live Premier League
Due to the Premier League winter break, Liverpool next play in the Premier League against Norwich on Saturday February 15 at 5.30pm, while Southampton host Burnley at 12.30pm the same day after their FA Cup replay away at Tottenham on Wednesday.