Honours were even at Selhurst Park as Burnley extended their unbeaten run to three games.
The Clarets are now just a solitary point from jumping out of the Premier League's relegation zone, though Everton were hosting leaders Manchester City in the evening kick off.
Sean Dyche, Manager of Burnley reacts during the Premier League match between Crystal Palace and Burnley at Selhurst Park on February 26, 2022 in London, England.
Sean Dyche's side also closed the gap on Leeds United and Brentford, who lost out to Tottenham Hotspur and Newcastle United respectively.
Burnley still have two games in hand on the Whites and three on the Bees, who continue to struggle in the top flight.
Reacted well to turn Olise's effort around the post when unsighted in the first half and beat away a stinging attempt from Zaha when the Ivorian threatened in the second. Let down by his defence for Palace's early opener.
Jeffrey Schlupp put Crystal Palace ahead inside the opening 10 minutes when turning Michael Olise's cross beyond Pope with an outstretched leg.
However, Luka Milivojevic handed the visitors a share of the spoils when touching Aaron Lennon's pull back into his own net.
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Given his toughest test to date when faced with the trickery and pace of Zaha. The Palace forward was able to drift in from the left hand side uncontested and beat the Burnley full back twice when going close to restoring his side's lead in the second half. However, the Welshman supplied the ball into Rodriguez for the equaliser.
Not at the races at Selhurst Park after a physically demanding week, which concluded with injury. The Dutchman was unable to halt Olise's run in the build up to Schlupp's goal and continued to struggle against the ex-Reading winger. Replaced by Taylor on the hour.
