After netting against Liverpool in midweek following his arrival from Real Sociedad, record signing Alexander Isak went close to scoring in the first half, robbing Joachim Andersen but failing to get his chip over Vicente Guaita when one-on-one with the Palace keeper.
Newcastle's Miguel Almiron went even closer, firing through a thicket of bodies and hitting the base of the post as the sides somehow went into the break level despite a slew of chances.
The home side thought they had taken the lead six minutes into the second half thanks to an own goal from Tyrick Mitchell, but the goal was ruled out after a VAR review found that Joe Willock had fouled Guaita.
Newcastle manager Eddie Howe said he could not believe his team failed to score.
"It was an incredible game," Howe told the BBC. "Two teams going at it trying to deliver. Barring a slow start -- or maybe a 15-20 minute period in the middle of the first-half -- the lads gave me everything. How have we not scored?"
Palace created plenty of opportunities of their own but many of them were fired straight at Newcastle keeper Nick Pope, who had little trouble dealing with most of them.
He did, however, pull off a tremendous reflex save in the 73rd minute to maintain his clean sheet.
Despite the two sides racking up 38 shots between them, the game finished scoreless to leave Newcastle in 11th position in the table on seven points, with Palace 15th on six points.
Midfielder Willock, who spurned two glorious chances to break the deadlock in the second half, was disappointed that his side could not manage to get more than a point.
"We had loads of chances and we have to put them away. We have to be clinical when you have a team by the scruff of the neck," the 23-year-old said.
Palace defender Andersen seemed happier with the point.
"It was not our best game with the ball, but the way we defended and the resilience we showed was fantastic," Andersen said.
"We need to see out these games -- if we don't win, we need to make sure we don't lose."