Liverpool, who have not lost to their neighbours for five years, went ahead in the 42nd minute when Danny Ings was left unmarked to head in a corner.
But in added time at the end of the first half, Belgium's Romelu Lukaku drove in the equaliser.
The draw left Everton one point in front of their old rivals but relieved some of the pressure on opposing manager Brendan Rodgers by extending his team's unbeaten record to six games.
It was a fair result in a game that never touched the heights of quality or excitement seen in many of the previous meetings.
Liverpool made all the early running and the home side's American international goalkeeper Tim Howard was forced to save twice from James Milner.
He was at fault, however, when Liverpool took the lead. Howard failed to come for Milner's corner and Ings, called into the England squad three days earlier, was all alone as he headed in.
Everton had improved in the meantime, Steven Naismith's header and James McCarthy's drive demanding good saves from Simon Mignolet.
And in added time at the end of the first half, Lukaku drove in the equaliser after Emre Can failed to clear a cross.
That sent the Blues into the dressing-room and out again with a spring in their step. They gained further momentum by sending on former Tottenham winger Aaron Lennon for Gerard Deulofeu, although clear chances were hard to come by.
Ross Barkley ran at the Liverpool defence before shooting narrowly wide and soon afterwards Lukaku's drive went straight at Mignolet from a promising position.
The visitors were reduced to counter-attacking and with Philippe Coutinho's shot comfortably saved by Howard, Rodgers sent on Adam Lallana for Ings, plus Joe Allen for Lucas Leiva.
The fixture has produced more red cards than any other (20) since the Premier League began in 1992 and Everton felt there should have been one for Brazilian midfielder Lucas.
He escaped with a yellow, along with team-mate Can and Mamadou Sakho, plus Everton's Barkley, James McCarthy and Lukaku.
Rodgers told reporters he did not feel under any pressure and was "really proud" of his players.
"It is a very good point," he added. "It is a difficult place to come. We looked like we were getting better in our attack and defensively we were more cohesive."
Everton manager Roberto Martinez felt his team deserved to win.
"Every time we had the ball in their half, we looked like creating something," he said. "Mignolet made two outstanding saves. We are disappointed with the goal we conceded."
(editing by Alan Baldwin)
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