Roberto Firmino’s first half goal secured a battling 1-0 win at Tottenham Hotspur for them.
Juergen Klopp’s unbeaten side were not at their best and had to withstand a Spurs fightback after the break.
But they hung on for a 20th win out of 21 league games this season to move further ahead of second-placed Leicester City with a game in hand.
Liverpool’s total of 61 points is the most after 21 games of a Premier League season, beating Manchester City’s 59 from two seasons ago.
It is a record that has never been surpassed in the Spanish, Italian, German or French leagues at the same stage.
Firmino’s 37th-minute effort proved enough for Liverpool to march on towards a first English title since 1989/1990.
But Tottenham substitute Giovani Lo Celso wasted a glorious chance to earn the hosts a draw with a glaring late miss.
Liverpool’s fans stood to acclaim their side at the end.
Spurs manager Jose Mourinho, who has now won only two of 11 games against Liverpool boss Juergen Klopp, shook hands with every opposition player at the final whistle.
“I’m over the moon about the result, but we have to talk about the performance,” a rather subdued Klopp said later.
“One team deserved to win and that was us. To win at Tottenham is pretty special. That the game wasn’t decided after 50-60 minutes was our fault. We should have scored more goals.
“We were on the ground towards the end. A couple of our players were slightly exhausted, but we fought through that,” he added after his side stretched their lead over Leicester, who had earlier lost 2-1 at home to Southampton.
Klopp’s unstoppable side are now unbeaten in a club record 38 league games.
Tottenham, who in June faced Liverpool in the UEFA Champions League final in Madrid, are drifting in eighth place, nine points behind fourth-placed Chelsea.
Liverpool dominated the first half and it needed a superb block by Tottenham’s 20-year-old defender Japhet Tanganga, handed his first league start, to deny Firmino.
Alex Oxlade-Chamberlain could only hit the rebound against the post.
Liverpool defender Virgil van Dijk then looked certain to head in Jordan Henderson’s dinked cross but goalkeeper Paulo Gazzaniga made a superb reflex save.
With Tottenham sitting deeper and deeper, the pressure finally told as they failed to clear the ball and Mohamed Salah’s pass evaded Tanganga for Firmino to fire past the stranded Gazzaniga.
Spurs, without their injured talisman Harry Kane, were far more lively after the break as Liverpool’s pace slowed.
Son Heung-min wasted a great chance to equalise, curling the ball over the bar after Liverpool were caught in possession.
Then, substitute Giovani Lo Celso somehow missed the target with the goal gaping after being picked out by Serge Aurier.
Erik Lamela also came off the bench and tested Liverpool goalkeeper Alisson, but the Reds showed incredible defensive discipline to record a sixth successive clean sheet.