The opening 20 minutes or so were quite back and forth with teams sharing possession of the ball. The highlight of the early goings may have been a nice save by the much maligned goalkeeper Tim Howard.
On the 21st minute, Romelu Lukaku beat Wayne Hennessey, the Palace keeper, but couldn't beat the post.
Throughout the remainder of the first half, the Toffees bossed possession, but were unable to put together the final pass and put a man in on goal.
The second half maintained the break neck pace of the first 45 minutes.
Palace had a penalty shout in the 53rd minute when Gareth Barry took down Mile Jedinak by his shirt on a corner kick. It happened right in front of the referee but nothing was given.
It was Everton again who almost got on the board, this time via a near own goal. Ross Barkley took a free kick and smacked a line drive into the box. Palace striker Connor Wickham put his head in the way and just about put the ball in his own net. Instead, it pinged off the crossbar and back into play.
A few minutes later, the hosts had yet another chance on goal. Set up by a pretty Lukaku lay off, Tom Cleverly perfectly struck a volley toward the Palace net, but Hennessey was up for the task and parried it away.
It continued on with Everton getting the best of Palace for most of the half until the Eagles did what they do. They had a breakaway and put a shot on goal, which Howard blocked over the end line for a corner. But on that corner, Scott Dann rose like a salmon and put the ball in the net to give the visitors a 1-0 lead in the 76th minute.
The Blues did fight back. Three minutes later, Lukaku had another ball go off the woodwork. This time it was a half-volley that went up and over Hennessy and then off the crossbar.
Then, in the 81st minute, the big Belgian finally got the goal that both he and the club deserved. Of course, it was a hard hit ground ball off the foot of Gerard Deulofeu across the mouth of goal right onto the left foot of Lukaku, making it 1-1 with nine minutes to play. Lukaku now has 50 goals in 100 appearances for Everton.
Those final minutes were packed with antsy moments, but no chances on goal for either side. Everton seemed to be the bigger threat, but their eagerness for a winner did open up space for Palace to counter, which they did little with in the end.
It was clear to anyone watching that Everton were the better team on the pitch by a good margin. According to the BBC, they had 62 percent possession, had 19 shots and 13 corners. The problem was that only four of the shots were on target and, really, they could have had even more chances if the final pass was there.
Also, manager Roberto Martinez made just one substitute as Leighton Baines returned to Premier League action in the 62nd minute in place of Brendan Galloway. Meanwhile, the attacking likes of Kevin Mirallas, Steven Naismith and Aaron Lennon remained on the bench. This is a matter of opinion, but taking off a more defensive option like Barry or someone else for one of those three for the last five minutes could have made a difference.
With the draw, Everton remain in ninth place in the league, now with 22 points. Next week, another game that they should expect to take three points from; a Saturday trip to play Norwich City.