Eddie Howe's side dominated in the first half with Joelinton twice having good chances, but they struggled to open up a dogged Palace side after the break at Selhurst Park.
In the end a draw was just about a fair result with Newcastle moving to 39 points from 20 games, ahead of Manchester United on goal difference. Palace stay 12th with 24 points.
It was a frustrating evening for Newcastle who will feel it was two points dropped in their quest for a top-four finish.
"I'm really pleased with the team today," Howe said. "We had the moments and the chances to score but we didn't take them. We were frustrated after but we have high expectations.
"Palace defended well."
They enjoyed the lion's share of possession and carved out most of the few clear chances on offer but lacked the cutting edge in their sixth 0-0 draw of the season.
Palace were worthy of a point as they continued a tricky run of fixtures which included a draw with Manchester United in midweek.
"We knew it would be difficult at Palace but maybe it was a missed opportunity, but it's a good point coming here," Newcastle right back Kieran Trippier said.
Newcastle were impressive in the early stages with Miguel Almiron volleying wide from a good position.
Callum Wilson wasted another good chance for Newcastle after the break, heading straight at Guaita.
Palace came closest to breaking the deadlock when the ball fell for Mateta on the bounce and he connected well, only for Pope to make an instinctive save.
Newcastle will now switch their attention to next week's League Cup semifinal first leg against Southampton.
- Craig Pawson
|Brighton & Hove Albion||6||5||0||1||+10||15|
|West Ham United||6||3||1||2||+1||10|