Victor Anichebe, whose earlier header had appeared to cross the line but was not given, thought he had won it three minutes from time but Demba Ba scored his second of the night even later.
Leighton Baines had put the hosts ahead in the 15th minute only for Ba, on as a second-half substitute, to score with virtually his first touch after coming on at half-time.
Marouane Fellaini's effort was ruled out on a questionable offside decision before Anichebe, also brought off the bench, had a goal disallowed to add to the controversy.
While post-match discussion will be all about technology and officials' decisions, the pre-match focus was on recognising the fight of Hillsborough campaigners in their battle for justice after the publication of last week's independent report.
The club's approach was pitched perfectly as, in addition to two mascots wearing an Everton No.9 nine shirt and a Liverpool top with the No.6 and ball boys bearing the No.96, the names of all victims of the disaster scrolled across Goodison's television screen accompanied by the Hollies' 'He Ain't Heavy . . . He's My Brother'.
But while Everton stand beside their neighbours over Hillsborough they are pulling away from them in the table. A draw extended the gap over 17th-placed Liverpool to five points. They have been imperious at home in the last six months and that was reflected in a one-sided first half.
Nikica Jelavic had an early goal disallowed for offside but it set the tempo and when the breakthrough came in the 15th minute it was no more than the hosts deserved.
A 17-pass move merely reflected Everton's dominance as Baines raced on to a backheel from Steven Pienaar to fire past Steve Harper.
Kevin Mirallas, the £6m summer signing impressing on his first league start, had a couple of good chances while Phil Jagielka shaved the post with a volley.
The loss of the Croatia striker with a knee injury just before the interval was a blow to Everton but not as much as Ba's equaliser after the break.
Within four minutes of being introduced the half-time substitute hit a low shot past Howard after Yohan Cabaye robbed Osman and rolled a perfectly weighted pass.
It was the first goal by an opposition player at Goodison Park since Thomas Vermaelen's winner for Arsenal on March 21.
Harper's sportsmanship did Victor Anichebe a favour when he made little of the forward's late sliding challenge, intimating to referee Michael Jones he did not have an issue with the tackle.
Marouane Fellaini had a goal ruled out for offside, a decision which was marginal at best, but only goalline technology – which does not come in until next season – could have assisted Jones when Anichebe's header was tipped on to the bar by Harper but bounced over the line before the ball was cleared.
Anichebe left no room for doubt three minutes from time when he turned in the area to fire home but Everton's celebrations were short-lived when Ba latched on to Shola Ameobi's knockdown to roll a shot under Howard.
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