Everton midfielder James Rodriguez's well-placed finish in the 56th minute gave the Toffees a deserved lead before Jeffrey Schlupp found Michy Batshuayi in space, who comfortably slotted the ball past Robin Olsen into the bottom corner of the net.
Here are some of the key talking points of the game:
A new Crystal Palace system:
Flashback to the 28th of February where Crystal Palace had to hold onto a 0-0 draw with Fulham at Selhurst Park. The team failed to register a shot on target and they were having to put in countless last ditch blocks and tackles. There was a complete lack of attacking prowess and the team hardly put any pressure on their opposition's defence.
That team looks so alien to the one that turned up at Goodison Park on Monday. From the start, Crystal Palace were playing some nice one-touch passes and they were looking to get forward at every opportunity.
Roy Hodgson's side looked so much more positive with their attacking play after the international break and they showed that with some good possession football and quick passing play to get up the pitch at speed. They also must have worked on their pressing play, making them strong when their opposition made loose passes or took a heavy touch.
Even with this new promising attacking play, the team struggled to find that final pass to create clear-cut chances in the first half but this promising first half performance meant that the teams went in goalless after the first 45 minutes.
In the second half, after Everton took the lead, their defence looked resolute and it looked likely that Crystal Palace would struggle to break through.
The Eagles were forced to shoot from distance with Eze, Ayew and Wilfried Zaha having long range strikes kept out by the Swedish keeper.
In the 82nd minute, Jeffrey Schlupp dragged a shot wide from inside the box and it looked like they had missed their chance to equalise but the midfielder made up for it when he threaded a great pass through to Michy Batshuayi, who scored the goal that Palace rightfully deserved.
They had a chance to grab all three points when Jean-Philippe Mateta tried to strike the ball into the roof of the net but Olsen was equal to it and the sides had to share the points.
A wasteful Everton:
In the sixth minute, Luka Milivojevic made a mistake in midfield, allowing Andre Gomes to dispossess him and set up a 2v2 position with Richarlison and Dominic Calvert-Lewin. But it was Gary Cahill who managed to block the latter striker's effort and this really set a precedent for the rest of the game.
After a shaky nervous start, Everton began to find their feet and a great long ball over the top found Calvert-Lewin through on goal, but Vicente Guaita came out quickly to close down the angle and smother his effort.
This was also the start of a long afternoon for the Blues and an even longer one for Richarlison, who headed over from six yards out and two minutes later, had two shots saved from Guaita, which really set the story for the rest of the match.
Richarlison struck a free-kick high and wide and then headed over from a free-kick minutes later, leaving the first half surprisingly goalless ahead of the second half.
Before Everton went 1-0 up, Gylfi Sigurdsson had a shot saved well from close range and Calvert-Lewin was inches from turning the rebound in before Seamus Coleman eventually set his teammate James Rodriguez up to fire low into the net.
Everton have struggled to win at Goodison Park as of late, and this is evident as even when they went 1-0 up, failing to strengthen their lead and kill the game off with more missed chances from their strikers.
Even when they conceded the equaliser, they had chances that could have been converted but Guaita managed to save again. The performance that Guaita put in was enough to get the Spanish keeper the Man of the Match award for Crystal Palace; vital in gaining a point for his side.
What's next for Crystal Palace?
This will prove to be a huge challenge for Roy Hodgson's men, even with their inspired performance at Goodison Park. Before last weekend, Thomas Tuchel's Chelsea were unbeaten and they still boast some brilliant talent even after their disappointing loss.
Roy Hodgson's side will need to be resolute in their defending as Chelsea won't be as wasteful with their shooting as Everton were.
It will also be quite interesting to see if this new system is used for the rest of the season or if it was specific for Everton. Some good attacking play will be needed though if they want to beat Chelsea, a team that are normally quite strong and regimented in their position - which makes them horrible to break down.