The Eagles have been relegated in each of their four previous Premier League seasons but Pulis, who has never been relegated in his managerial career, is determined to buck that trend.
Palace's fortunes have been transformed since the Welshman arrived in November and, with 26 points on board, they sit 14th ahead of Wednesday's trip to Everton.
This season's relegation battle looks set to be one of the tightest in top-flight history, but Pulis is confident his charges are up for the fight.
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"Ever since I became a manager in the Premier League, I think if you get to 40 points, you've got a massive chance of staying up.
"If you look at the table and see how many clubs are involved in it, there's 10 or 12 clubs who are involved. It's just keeping your nerve."
Pulis boosted his ranks with the signings of Tom Ince, Joe Ledley and Scott Dann in the January transfer window and the former Stoke boss is delighted with how quickly his new acquisitions have settled, with Ince and Ledley scoring in a 3-1 victory over West Brom at the weekend.
"The big worry is that they don't hit the ground running and they take time to settle," he continued. "In the position we're in, we haven't got a lot of time for them to settle in.
"It's nice that Joe and Incey scored and Scott played in a winning team.
"I think he (Ince) has got the ability to play in any of the front positions. He could play up front by himself.
"He's a clever player, he's got good feet and his movement's very good. You look at him as a player and you think he'll score goals. I was really pleased to see him get off the mark."