Liverpool - A freak injury-time goal from Liverpool substitute Divock Origi settled the Merseyside derby and kept Jurgen Klopp's unbeaten team hard on the heels of Premier League pacesetters Manchester City on Sunday.
The 1-0 victory extended Liverpool's unbeaten sequence in Merseyside derbies in the Premier League to 16 games although the manner of the winning goal made this one of the more unforgettable of those games.
In the 96th minute, Virgil van Dijk mishit a hopeful, desperate shot in the direction of the Everton goal with the effort ballooning into the air and the defender turning his back in disgust.
But Everton goalkeeper Jordan Pickford struggled to judge the ball as it dropped from the Anfield night sky.
With the ball looking as if it might hit the cross-bar, the England man pushed the ball upwards and presented Origi with a simple headed finish into an open net.
Liverpool thought they had won the game three minutes earlier when van Dijk headed on a corner and Origi turned a difficult chance onto the Everton bar, with home supporters appealing for a penalty after Daniel Sturridge's follow-up shot appeared to strike Gylfi Sigurdsson on the arm.
But how the 100th Anfield league derby still stood goalless at that stage was a surprise with the first half, especially, producing multiple chances for both teams.
A set-piece presented Everton with the game's first chance with just four minutes gone as Lucas Digne swung in a well-worked free-kick and defender Yerry Mina rose from a group of players but saw his attempt fly well wide.
Everton's other great first half chance owed more to spirited defending than poor finishing as Theo Walcott headed across goal and Andre Gomes looked certain to nod into the Liverpool net from close range.
Somehow, goalkeeper Alisson made an extraordinary reflex block and, after the ball rebounded against Gomes's head and looked destined to trickle over the goalline, it was Liverpool defender Joe Gomez who made a brilliant last-ditch clearance to hack the ball to safety.
Yet Liverpool, predictably, looked in the mood to continue a record that has seen them unbeaten in this home fixture for 19 years.
Xherdan Shaqiri squandered his team's best opening, played clean through by Mo Salah after 33 minutes but taking an extra touch that allowed Pickford to block his effort.
The tempo did not lessen after the restart. Salah, looking to score for a third consecutive league game, curled a shot just wide from 20 yards and Sadio Mane chased onto a Firmino through ball that Seamus Coleman failed to deal with, only to slide his shot wide.
Liverpool were beginning to dominate even more than had been in the case in the first half, Salah, yet again, creating an opening as he passed back to the edge of the area for Mane to miss the target.
But Marco Silva introduced young winger Ademola Lookman off the Everton bench and his side's attacking threat instantly improved.
Soon, Sigurdsson was forcing Alisson into a routine save from long range before Lookman set up Bernard for a shot which the Brazilian sent flying just wide of the right-hand upright from 20 yards.
By the 74th minute, Klopp was desperate for a change and brought on Sturridge to replace Salah, who did not look pleased at being replaced.