The gap between Liverpool and Leicester at the top remains eight points, but the Foxes are now three points clear of Manchester City in second and six ahead of Chelsea, who suffered a shock 0-1 home defeat by West Ham.
Tottenham are up to fifth as they ride the wave of Jose Mourinho's arrival, but Manchester United and Arsenal dropped more points in 2-2 draws with Aston Villa and Norwich respectively.
The only Premier League match Liverpool have won by more than a single goal since mid-September was against City last month and even after Virgil van Dijk's early double at home to Brighton on Saturday (Nov 30) they had to endure a nervy finale.
Goalkeeper Alisson Becker's red card and Lewis Dunk's clever free-kick made the European champions sweat in the final stages, but they dug in and held on in a manner that has characterised their charge towards a first title in 30 years.
"The boys threw everything on the pitch," said a delighted Liverpool manager Jurgen Klopp. "It's unbelievable how much they want to win."
By contrast, when the going has got tough, City have not got going.
Saturday's 2-2 draw at Newcastle was the fifth time Pep Guardiola's men have conceded two or more goals this season and on each occasion they have dropped points.
Worse could even be still to be come. After a tricky trip to Burnley on Tuesday (Dec 3), City face five of the top nine before the new year.
What a difference a week makes for Tottenham. Three games into Mourinho's reign and three wins have booked Spurs' place in the last 16 of the Champions League and enlivened their chase of Chelsea to make it back into the competition next season.
Mourinho's men are now within six points of his old side after a 3-2 victory over Bournemouth that was far more convincing than the scoreline suggests.
"When I arrived we were 12 points behind the Champions League positions and I said 'I don't want to think about it, I just want to play matches.'" said Mourinho. "If we think too much about it we are going to be depressed because we want to play European football next season."
Now the Portuguese smells blood and has two of his former employers in his sights.
Spurs travel to Manchester United, who sacked Mourinho 11 months ago, on Wednesday (Dec 4) and host Chelsea in three weeks' time.
"We play Chelsea by the end of December. If we play them tomorrow, it is with six points difference, it would be a fantastic situation to play them. But we play them in the end of December and we have to keep as close as possible."
Just over a week after Mourinho replaced the fired Mauricio Pochettino, there was also change across north London as Arsenal sacked Unai Emery on Friday (Nov 29).
Less than 48 hours later, Quique Sanchez Flores became the latest Premier League manager to lose his job after Watford fell to the bottom of the table with a 2-1 defeat at fellow strugglers Southampton.
Marco Silva could soon follow as Everton were undone by Kelechi Iheanacho's stoppage-time winner for Leicester to slip just two points above the relegation zone ahead of Wednesday's trip to Liverpool in the Merseyside derby.
However, the Toffees may take note of West Ham's decision to give Manuel Pellegrini an extra week to turn around his side's fortunes.
The Hammers travelled to Stamford Bridge on an eight-game winless run, but were the perfect blend of disciplined in defence and dangerous on the counter-attack to hold Chelsea scoreless in the Premier League for the first time since the opening weekend of the season.
In other results Crystal Palace won 0-2 at Burnley and Wolverhampton Wanderers and Sheffield United played out a 1-1 draw at Molineux.