Steven Gerrard took the lead for the home side on 68 minutes, before Tim Cahill stunned the Kop with an 87th minute equalizer.
Rafael Benitez’s men are now joint leaders with Manchester United on 47 points. However the latter still have one more game in hand.
Everton had the first chance of the game, when Victor Anichebe fired a surprising left footed effort from outside the box. Giuseppe Reina was alert to tip around the post.
However, it was Fernando Torres who produced one of the misses of the season, when he was released through on goal by a Sami Hyppia long ball.
The Spaniard took all the time in the world before placing his shot off the Everton post and deny Liverpool from taking a much needed lead.
After the interval, Gerrard came to his team’s rescue, when he ended a typical long run from midfield with a powerful shot pas Tim Howard to put Liverpool ahead.
Everton levelled the score three minutes from time when they were awarded a free kick from outside the box.
Mikel Arteta stepped up and his cross was met by Cahill’s header to shatter their arch-rivals hopes of retaining the Premiership’s summit.
Everton are currently sixth in the table with 36 points after 22 games.