Pulis: Palace not safe yet
Back-to-back wins over Chelsea and Cardiff City have seen Palace climb to 14th in the table, and the London club have a game in hand over four of the six teams below them.
But despite the apparent safety of their position, former Stoke City boss Pulis has warned their situation could change very quickly between now and the end of the season.
"When can you relax? Not until we're safe, until we're mathematically safe," he said.
"I don't think that will be this weekend, or the weekend after that or maybe even after that.
"You just worry to death about getting over that line, you won't change that.
"There's more twists and turns in it. We're desperately keen to get as many points as we can."
Palace welcome Aston Villa to Selhurst Park on Saturday, and will hope for a repeat of the reverse fixture on Boxing Day, when Dwight Gayle's stoppage-time strike sealed a 1-0 win.
The 23-year-old has slowly been making his return to the fold after an ankle injury, and scored five goals in an under-21 fixture against Brentford on Tuesday.
However despite that showing, Pulis said he would bide his time with the striker.
"I went and watched the game, Gayley did well," he said.
"Gayley's very good around the place, he's desperate for his chance. To score five goals - and I know it's against Brentford in a reserve game - was fantastic ... (but) I'm not going to put Gayley in because of that game."