Wilfred Zaha missed several scoring opportunities in their 30 attempts on goal for Palace
Ghanaian duo of Jordan Ayew and Jeffery Schlupp were on the bench for Crystal Palace as Cardiff survived a barrage to gain only their second point of the season on their travels and edged clear of the Premier League relegation zone.
Andros Townsend flicked a shot against the crossbar and Luka Milivojevic hit the post for the hosts who dominated possession but disappointed in front of goal.
Cardiff though, still smarting from their 5-1 defeat to Manchester United, delivered the sort of performance that Neil Warnock sides are renowned for - doggedly defending and attempting to counter when possible.
And while Palace had 31 shots on goal, they failed to build upon their clinical victory at Manchester City four days ago.
Cardiff had limited opportunities to score, and they were denied the ultimate smash-and-grab victory by Palace keeper Vicente Guaita, who superbly saved from Kadeem Harris at point blank range.
The result leaves Palace in 14th place on 19 points while Cardiff remain 17th on 15 points.
Wilf Zaha and Luka Milivojevic again played the role of main protagonists for Palace who controlled proceedings without delivering the precise finishing that upset Pep Guardiola's side four days ago.
Schlupp who was the hero in Palace win over Man City over the weekend was left on the bench along with his countryman Ayew who has struggled to impress for the London side this term.