A see-saw encounter at Goodison Park finished honours even, but could have gone either way with both clubs having chances to take all three points even after Sturridge's 89th-minute strike.
The Toffees climb to fifth in the table, three points behind their city rivals who stay second.
England striker Sturridge was not deemed fit enough to start for the Reds after playing 90 minutes against Germany in midweek with a dead leg.
Prior to his intervention, it appeared Everton's Kevin Mirallas would be the man to remember as the home side twice came from behind.
The Belgium international may have been outdone by compatriot Romelu Lukaku, who scored twice in the second half, but he had a hand in all three goals.
However, the debate will rage as to whether he should have been on the pitch for the last two assists for a knee-high challenge on Luis Suarez which could - and probably should - have seen red.
The scoring started after just five minutes. Steven Gerrard swung over a cross from the left, Suarez could not get the significant touch to direct it goalwards but it was enough to send it to Philippe Coutinho who smashed home a shot at the far post.
But within three minutes, Ross Barkley somehow got to Leighton Baines' free-kick ahead of Martin Skrtel and diverted it to Mirallas who nipped in front of Gerrard to stab home.
That was the boost the home side needed and, when Lukaku raced forward after Steven Pienaar had robbed Gerrard on halfway, only the speed of goalkeeper Simon Mignolet coming off his line snuffed out the danger.
However, Liverpool regained the advantage on 19 minutes. Fouled by James McCarthy, Suarez picked himself up to curl a brilliant free-kick through the tiny gap left between the end of the wall and Pienaar. Tim Howard appeared to have it covered but some late spin saw it creep in.
Mirallas then sparked what could have been a pivotal moment when he clattered into Suarez's right knee as the pair challenged for the ball leaving his opponent in a heap on the floor.
The only excuse referee Phil Dowd could surely have had for just showing a yellow card was that he was unsighted.
While the Liverpool striker eventually lasted 90 minutes, Baines did not and just after the break was substituted, with a suspected broken toe, for the first time in the league since 2008.
With Gareth Barry moving to left-back, substitute Gerard Deulofeu, on loan from Barcelona, had the chance to make himself an instant hero after outpacing the defence but mis-hit his shot and Mignolet saved.
Joe Allen, starting his first Premier League match since March, could have put the game to bed after Suarez's dribble fell to him with only Howard to beat but from 10 yards out he missed the target.
Mignolet was the goalkeeper who was by far the busier and he denied Lukaku three times as Everton pushed for the equaliser.
However, from the last effort the Belgium international could only parry his compatriot's free-kick and, when Mirallas crossed back in, Lukaku seized on McCarthy's deflection to ram home.
Still the chances came; Howard producing a brilliant block to keep out Suarez's close-range header and Mignolet denying Deulofeu.
But there was no stopping Lukaku's powerful header from a corner - taken by Mirallas - eight minutes from time.
That appeared to have settled it until Sturridge nodded home Gerrard's free-kick to level it up again.
In stoppage-time, Victor Moses headed just wide from Suarez's cross, and Sturridge had the ball in the back of the net again only for the goal to be disallowed for offside.
And at the other end, Deulofeu was again denied by Mignolet while McCarthy's final shot was blocked for a corner before Dowd brought an end to proceedings.