Dominic Calvert-Lewin struck late on as 10-man Everton twice came from behind to hold Liverpool.in a 2-2 encounter.
Sadio Mane gave Liverpool a third-minute lead, converting a cross from the rampaging Andrew Robertson.
But after Virgil van Dijk had limped off, Michael Keane headed in James Rodriguez's corner on 19 minutes for Everton's first Goodison derby goal in five seasons.
After half-time, Richarlison hit a post, before Mohamed Salah's spectacular shot on 72 minutes made it 2-1 for his 100th goal for Liverpool.
With nine minutes remaining, Calvert-Lewin headed in Lucas Digne's cross but then Richarlison was sent off for a foul on Thiago.
Jordan Henderson thought he had won it for the champions in stoppage time, but his effort was overturned by the VAR for offside.
The striker, Dominic Calvert-Lewin is redefining expectations and so, progressively, are Everton.
Nine minutes remained, Everton were trailing 2-1 and appeared poised for a first defeat of the season.
Then Lucas Digne flew down the left to fasten onto James Rodriguez's slide-rule pass and hang up an inviting cross.
Calvert-Lewin's directed his header into the turf and beyond Adrian's dive to his left.
That wasn't the half of it - nor was it the end of it.
Richarlison, who had hit the post with a header, was red carded for a challenge on Sadio Mane in the 90th minute.
In the third of five minutes of time added on Liverpool thought they'd won it but the VAR detected Sadio Mane, who scored Liverpool's first goal - had strayed marginally offside before centring for Jordan Henderson to finish.
Michael Keane had supplied Everton's first equaliser, Mohamed Salah thumping Liverpool back in front on 72 minutes.