Liverpool's haul of 60 points from 23 matches tops the Reds' previous best tally of 59.
Saturday's early kick-off saw teenage midfielder Declan Rice score his first West Ham goal in a 1-0 win at home to London rivals Arsenal.
Aaron Ramsey is already free to sign a pre-contract agreement with foreign clubs.
There was one 'giant-killing' on Saturday with third-tier Gillingham beating Premier League Cardiff 1-0.
Chelsea remain in fourth place, but they are now just three points ahead of fifth placed Arsenal in the race to qualify for next season's Champions League.
Swiss midfielder Granit Xhaka had set Arsenal on their way with his fourth goal of the season.
Manchester City now trail Liverpool by 10 points.
Jeffrey Schlupp, Andros Townsend and Luka Milivojevic were the goal scorers for Crystal Palace.
Apart from Pierre-Emerick Aubameyang, substitute Alex Iwobi scored the third goal for Arsenal while Ashley Barnes scored the lone goal for Burnley.
Son Heung-Min put Tottenham ahead and Alli increased their advantage as they won at the Emirates Stadium for the first time in 10 visits.
Southampton had twice taken the lead through Danny Ings.
Manchester United have an impressive recent record against Liverpool, unbeaten in eight league games.
Arsenal overcame a resolute Huddersfield to stretch their unbeaten run to 21 games.
Manager Jose Mourinho made four changes to the side against Fulham after their draw with Arsenal in midweek.
A video has emerged that appears to show a number of Arsenal stars inhaling nitrous oxide.
Chelsea and Arsenal are now tied on 31 points in fourth, still eight clear of United in eighth.
A banana skin was hurled from the away end at the Emirates Stadium as Pierre-Emerick Aubameyang celebrated scoring in front of the Tottenham fans.