The match was quite scrappy throughout, perhaps as expected in a meeting between two bitter rivals.
Neither side created a significant number of scoring opportunities, with both defending their box well.
Brighton were awarded a penalty midway through the second half, but Georginio Rutter was deemed to have initiated contact with Jaydee Canvot.
The draw meant neither team left with the bragging rights, and the hosts remain one point ahead of Brighton in the Premier League table.
Story of the match
Fabian Hürzeler named the same team that beat Leeds 3-0 at The Amex last weekend.
Meanwhile, there were two changes to Crystal Palace’s last Premier League starting lineup, with Adam Wharton returning to the side and teenage centre-back Canvot replacing the absent Marc Guehi.
It was an end-to-end affair in the early stage,s with neither team able to take control and calm the game down.
The first clear chance fell to Jean-Philippe Mateta, whose shot flew over the crossbar as he attempted to beat Bart Verbruggen at his near post.
Soon after, Brighton made their way up the pitch with a beautiful passing move which almost culminated in a tap-in for Danny Welbeck, if not for Maxence Lacroix’s interception.
Both goalkeepers were forced into saves in quick succession before the match began to slow down, and each team struggled to create.
Brighton had the larger share of possession, but Palace were disruptive in midfield, and the Seagulls were unable to consistently make their way into the final third.
The home side were more reliant on set pieces and, in particular, long throws to endanger their rivals. However, Brighton’s aerial defending was good, and they dealt with the threat well.
Palace recognised the danger that Yankuba Minteh could pose if given space, and managed to limit him for almost the entirety of the first half.
The winger did find room to deliver a few excellent crosses early in the second half. There were numbers in the box for Brighton but none of Minteh’s teammates could connect with his crosses.
It looked as though the Eagles would finally open the scoring not long after, but Ismaïla Sarr could not sort his feet out.
Daichi Kamada had a chance for his first Premier League goal on the follow-up, but his effort went wide.
After Minteh found some more joy at the start of the second half, Tyrick Mitchell continued to limit him effectively - with the help of Canvot.
The French defender was initially penalised for a foul on Rutter in the penalty box. However, the penalty was ruled out by VAR, and the Brighton forward was given a yellow card for simulation.
Yeremy Pino replaced Adam Wharton in an attacking change for Palace, but missed a chance to test Verbruggen when the ball immediately fell to him in front of goal
Palace’s European endeavours appeared to be catching up with them towards the end of the match, not able to maintain the intensity they had played with earlier in the match.
Pino had another chance to win the match in the final minutes of stoppage time, another attempt at Verbruggen’s near post which the Dutch ‘keeper pushed around the post.
Mitchell up against Brighton's Georginio Rutter. Source: Ben Stanstall - AFP
Palace’s wing-back faced a tough task on their left flank in Minteh: Brighton’s top assist provider so far this season.
Aided by Canvot’s impressive display on his first Premier League start, he was able to limit the space that the Brighton winger had to operate in.
Mitchell’s contributions going forward were also evident, particularly when Pino was introduced, and he was able to combine with a more forward-thinking player.
His positioning was excellent in and out of possession during the match as he retained control over his side of the pitch throughout.