Jurgen Klopp's unbeaten side looked set to drop a precious two points in their dogged pursuit of City but they benefited from a freakish error from Everton goalkeeper Jordan Pickford to win 1-0 and continue their Anfield hex over their city rivals.
Spurs dropped out of the top four entirely after Match Day 14, after they were beaten 4-2 by Arsenal in a pulsating North London Derby at The Emirates.
That 2-1 defeat was a setback to Klopp's side in the Champions League, but Liverpool remain unbeaten in the Premier League this season.
In the Merseyside derby, the visitors missed an opportunity for an early lead when Yerry Mina's header from a free-kick narrowly missed the far of the left hand post.
With the games coming thick and fast over the festive period, he is likely to be handed a second chance before the transfer window reopens.
Jurgen Klopp knows Liverpool are lacking the fluency of last season, but hopes focusing first on defending will pay off eventually.
Pickford apologised for his blunder but gave a different version of events. We knew how strong they were but today they were outstandingly strong and hard with the way they played.
Fellow pundit Graeme Souness, who played for and managed Liverpool, said Marco Silva's side had set down a marker of the level of performance the club should expect from big away games, having held a Liverpool team chasing the title so well for 95 minutes.
Klopp ran onto the pitch after the goal
"What can I say about it?" "It was not in my plan".
Klopp sprinted onto the pitch when the ball hit the net where he hugged his goalkeeper Alisson. "Not cool, but it happened".
In defence of Allardyce, the former England manager was tasked with keeping Everton up and he did just that, but there was precious little flair or entertainment on offer at Goodison Park last season.
"But to be honest for me it is quite odd".
But Aubameyang's superb long-range equaliser sparked a second half surge from the Gunners.
"Yes, in specific games we can say that", he said.
We have to be together. This is more than being about a derby win, it's about keeping in touch with Manchester City.
Pedro Rodriguez and Ruben Loftus-Cheek grabbed the goals as Chelsea bounced back from their first league loss last weekend at Tottenham by once again beating Fulham.
Pierre-Emerick Aubameyang converted a penalty in the 10th minute to put Arsenal ahead. They'll have the disappointment of losing the way they lost, but the way they turned up, there is no inferiority complex.
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Chance of rain mixing with snow later today
The unseasonably cool conditions will linger throughout the work week, with afternoon highs staying in the 30s and 40s. Temperatures will range from the 40s north and west to the 50s across southeastern MA, with a gusty southeast wind.
NYPD hunt couple who lost ring during romantic proposal
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