The Reds made the short trip across Stanley Park looking for only their third win of the season and found themselves in wonderland after only 20 minutes when they were two goals up before the Toffees came roaring back in an entertaining contest.
It took the visitors just 14 minutes to open the scoring, Jose Enrique made a surging run down the left-hand side before squaring the ball across the six-yard box where it appeared youngster Raheem Sterling would apply the finish had it not been for a push in the back. The ball squirmed out to Luis Suarez to drive home thanks to a big deflection off Leighton Baines.
Controversy always seems to surround Man of the Match Suarez and did so again when he celebrated Liverpool's first goal directly in front of David Moyes' technical area with a comical swan dive. He will see it as payback for the Everton manager's criticism of the Uruguayan's tendency to go down to easily.
The away fans found themselves in pandemonium six minutes later when that man Suarez glanced a header into the net from a trademark Steven Gerrard delivery.
It could have been easy for the Toffees to crumble but they recoiled under a minute later with Reds deputy keeper Brad Jones punching a corner clear only for Leon Osman to hammer home on the half volley from outside the area.
Goodison Park was rocking again when Everton grabbed a deserved equaliser after 34 minutes with Belgian duo Kevin Mirallas and Marouane Fellaini combining on the left side before the latter squared for Steven Naismith to fire home from close range for his first goal for Everton since joining from Rangers in the summer.
The second half turned into a staunch affair with both sides coming out with better shape defensively. That said Suarez thought he had won the game in stoppage time only for it to be wrongly ruled out for offside.
The point a piece leaves Everton in fifth place in the league whilst their great local rivals find themselves in 13th with only two wins from eight games.
Goodison Park, Liverpool - 39,613