Leighton Baines' own goal and Luis Suarez's header were cancelled out by Leon Osman and Steven Naismith in a helter-skelter opening half, with Suarez's injury-time disallowed effort adding late controversy.
Kevin Mirallas created early danger when he weaved his way down the inside-left channel but Martin Skrtel was on hand to cut out his driven cross.
Moments later Jose Enrique skipped free down the left and his delivery found its way to Suarez, whose drilled cross-shot flew in off the back of Baines' leg (14).
If Suarez's celebratory swan dive in front of the home bench angered the Everton faithful, their mood darkened further when the Uruguayan stole in to glance home a header from Steven Gerrard's free-kick (20).
Osman (22) gave the home side an instant lift as Brad Jones' weak punch fell perfectly for the Everton midfielder to slot home from 18 yards, courtesy of a slight deflection off Joe Allen.
Suarez was threatening at the other end while Jones was again unconvincing dealing with a high ball under pressure as both defences looked bereft of confidence.
The Liverpool keeper was helpless when Naismith timed his run perfectly to meet Marouane Fellaini's clipped cross to claim the equaliser with his first goal for Everton (35).
Andre Wisdom's cross just eluded Suarez but Raheem Sterling then produced a horrendous shank when clean through on Tim Howard.
The Everton keeper parried Gerrard's long-range free-kick while Nikica Jelavic, who had struggled all afternoon, planted a free header wide.
A prone Phil Jagielka denied Gerrard a late winner while Baines had to be alert to deny a darting Suarez as ill-will trumped skill in a niggly final quarter.Suarez thought he had won it deep in added time as he latched onto Sebastian Coates' knockdown, but his flicked finish was ruled out for a debatable offside decision.
|2||1st Half Goals||2|
|4||Shots on Target||3|
|9||Shots off Target||8|
|55.9||1st Half Poss.||44.1|
|56.2||2nd Half Poss.||43.8|