Romelu Lukaku put the hosts in front with a lovely free-kick, but moments into the second half, Beneke headed home to level – with no one else managing to hit the back of the net in what was a frenetic game.
Everton dominated the opening stages, and Lukaku came closest to opening the scoring inside the first 10 minutes – but he failed to divert Bolasie’s cross into the back of the net.
Zaha, lively on the flank, won a foul which led to Palace’s first real chance. However, Christian Benteke could only head wide from Puncheon’s resultant free-kick.
It was a manic clash, consisting of end-to-end attacks – though with little real quality in the final third.
Townsend struck a free-kick at the wall, as neither keeper was forced to make a save of note passing the half-hour mark.
But 35 minutes in, the deadlock was broken – Lukaku curling a free-kick over the Crystal Palace wall and into the corner of the net from 20 yards.
Coleman drove forward with the aim of creating another chance, but was stewarded out of play, before Barkley wasted a free-kick on the verge of half-time with the break coming and the Toffees retaining their one-goal advantage.
But just moments after the restart the score was levelled, Benteke curling a wonderful header past Stekelenburg from Kelly’s cross.
Gueye immediately missed a glorious opportunity to send the hosts back in front, but failed to convert Bolasie’s excellent cut-back, before Delaney netted a header for Palace – which was incorrectly ruled out for offside.
Puncheon cleared a Gareth Barry header off the line, as the game continue at a frenetic pace – but the attackign quality dropped to the level shown in the first-half.
There were half chances for both sides, and James Tomkins wasted a glorious opportunity from a few yards out, while Lukaku smashed over from inside the penalty area.
But the scores remained the same, and the final whistle went with both sides leaving Goodison Park with a point to their name.