Both clubs were promoted from the Championship last season and while Palace sit five points above the relegation zone, Cardiff are three points from safety in 18th place.
Palace gave themselves a real chance of surviving the drop when they stunned Chelsea 1-0 last weekend while Cardiff have struggled for points and consistency since Ole Gunnar Solskjaer replaced Malky Mackay in January.
“It was wonderful to see Cardiff get promoted last year,” Pulis said in Thursday’s news conference ahead of the game.
“It was a really good year for Welsh football (with Swansea winning the League Cup) and I want it to thrive. It’s a great club, a fantastic city and you hope that they stay in the Premier League along with us.”
Pulis has done well at Selhurst Park since he arrived in November following the departure of Ian Holloway.
Palace were languishing in 19th then but seven wins and three draws in the 19 games since has lifted them to 16th in the table and they have a reasonable chance of enjoying a second successive season in the Premier League for the first time.
Palace were relegated from the Premier League in its inaugural season in 1992-93 and on each occasion they have been promoted since – 1994-95, 1997-98 and 2004-05 – they were unable to avoid an immediate drop back down to the division below.
After his side lost to Palace last week, Chelsea boss Jose Mourinho said Pulis should win the Manager of the Year award if he kept the Londoners up, and the Welshman joked: “He knows what he is talking about.”
Pulis also praised his players for their response to his guidance.
“For Mourinho to take the time out to say well done to our lads shows great esteem from him as a man and a manager,” Pulis added.
“The biggest compliment I can pay to my players is their spirit and togetherness. This group has been exceptional.
“But we have to keep going and going and going until we are mathematically safe.”
He added that talks with goalkeeper Julian Speroni and other out of contract players would begin “once we know what league we are in”.
(Reporting by Mike Collett; Editing by John O’Brien)