Liverpool snatched a dramatic late win against Merseyside rivals thanks to a bizarre 96th minute goal from forgotten man Divock Origi.
Both sides had several good chances to score, but it was a self-inflicted error from Jordan Pickford deep in stoppage time that allowed Origi to grab a sensational winner that kept Liverpool within two points of Premier League leaders Manchester City.
The game had looked to be heading for stalemate before England No. 1 Pickford failed to deal with Virgil Van Dijk's mis-hit effort from the edge of the penalty area, leaving Origi to tap in from close range and extend Everton's 19-year wait for a win at Anfield.
Yerry Mina should have opened the scoring for Everton after four minutes with a free header from close range, but it bounced wide of Alisson's goal.
Liverpool then had a glorious chance of their own minutes later, with Mohamed Salah cleverly flicking the ball on for Sadio Mane to run in behind, but his half-volley was fired over.
Richarlison then made his way past the Liverpool defence with a weaving run, but stumbled as he was about to shoot and the chance went begging for Everton.
The away side continued to threaten, and again should have been in front when Andre Gomes headed goalwards from a few yards out, but Alisson denied him the opener.
An open game saw Liverpool create another big chance after Salah played in Xherdan Shaqiri, but his shot was saved at the near post by Pickford, before Theo Walcott rounded Alisson at the other end but the ball ricocheted wide.
The second half started at the same pace as the first, with Salah's curling effort going just wide and Mane scuffing his one-on-one.
Everton also had chances to take the lead, with Ademola Lookman skipping past several defenders before teeing up Bernard, whose shot went wide.
Naby Keita played Roberto Firmino through on goal late on but was unable to find the target, and substitute Origi hit the bar from a corner as Liverpool continued to push for a winner.
In the 96th minute, Van Dijk's sliced effort looped harmlessly towards the far side of the bar, but Pickford spilled the ball back into play and Origi was on hand to head in from a yard out to win it for Liverpool.