Luis Suarez created and scored goals in the opening 20 minutes to give the Reds a two-goal advantage but a few minutes later Leon Osman lashed onto goalkeeper Brad Jones' poor clearance to slot home.
David Moyes' side, undoubtedly, were the better side in the first half after conceding two goals. The equaliser came in the 35th minute through Steven Naismith who smashed in from close range.
Prior to the game, Moyes had blamed Suarez of turning people away from the game but the Uruguayan was denied a last-gasp winner. Sebastian Coates turned his header towards Suarez who toe-poked in from inches but linesman ruled out the goal for an offside.
Earlier, Suarez celebrated Liverpool's first goal by diving in front of the Everton manager which turned the match into an intense affair. The momentum turned towards the Toffees as Kevin Mirallas, deployed on the left-flank, continuously barged forward threatening Reds weak defence.
Mirallas had a huge impact on the game but had he not suffered an ankle injury during the first period, Everton could've sealed three points in this seasons first Merseyside derby.
However, youngest player on the field Raheem Sterling had a great chance to win it for Liverpool but the 17-year-old failed to test Tim Howard.
The Reds deserved all three points for Suarez's late winner but the linesman raised the flag rather belatedly to deny Brendan Rodgers his third win as Liverpool manager.
Everton maintained their fifth spot while their rivals are in a disappointing 12th place with 10 points after nine games.