The Magpies were unfortunate not to find themselves ahead at the half-time break, with Miguel Almirón hitting the post in a first-half consisting of multiple shots at goal for the hosts.
It looked as if Newcastle had taken the lead shortly after the restart through Tyrick Mitchell's own-goal but, following a controversial VAR review, the goal was disallowed as Joe Willock was adjudged to foul Vicente Guaita inside the penalty area despite replays showing the midfielder to be pushed by Mitchell into the Palace goalkeeper.
Despite a late flourish, Newcastle were unable to find a breakthrough as, despite extending their unbeaten start on home soil and recording a third clean sheet of the season, their winless league run extended to five matches.
Eddie Howe handed a first start on home soil to new signing Alexander Isak, with the Swedish striker netting on his highly-anticipated debut away at Liverpool on Wednesday night.
Centre-back pair Fabian Schär and Sven Botman both returned to the starting eleven in place of Jamaal Lascelles and Dan Burn, who played the full 90 minutes of the Magpies' midweek defeat at Anfield.
Isak spurned a glorious chance to send Newcastle ahead as the Swedish forward blocked Joachim Andersen's forward pass before racing through on goal but the 22-year-old elected for a deft chip, with Guaita standing tall to block the attempt.
Joelinton went close to recording his first Premier League goal since April as the Brazilian connected with Kieran Trippier's in-swinging cross from the right flank but his volley smashed off the side-netting.
Pope was on hand to prevent Jean-Philippe Mateta minutes later as the England international pushed away the Frenchman's stinging drive at goal before the striker's rebound was deflected behind for a corner.
Newcastle were unfortunate not to open the scoring as Sean Longstaff's header was parried by Guaita and after Cheick Doucouré swept the ball into Botman's path, the Dutch defender's close-range shot was blocked in a vast group of Palace defenders.
Almirón, who scored the winner in the last meeting with the Eagles in April, went close to recording his second goal of the 2022/23 campaign as the Paraguayan's strike from the edge of the box was deflected by Andersen before the ball clipped the foot of the right-hand post.
Newcastle continued their push for a breakthrough in the final minutes of the opening half as Botman was denied a first goal for the club since his arrival from LOSC Lille in July, as the centre-back's volley at the back-post was importantly pushed behind by Guaita.
In the second-half, Newcastle looked to have taken the lead as Botman's header across goal was inadvertently turned into his own net by Mitchell but, after a VAR assessment, referee Michael Salisbury chalked off the goal after Willock's collision with Guaita in the build-up, to the frustration of the home crowd.
Almirón squandered a golden opportunity to break the deadlock as the South American forward latched onto Longstaff's neat pass before dragging his effort wide of the target.
Pope produced a crucial stop to deny Palace substitute Odsonne Édouard and keep United on level terms, getting down low to turn the former Celtic striker's shot past the far left-hand post.
Willock missed two key chances in front of goal in the closing stages as the central midfielder controlled Isak's forward pass but saw his low shot saved by Guaita before the 22-year-old struck a close-range effort wide of the post after making contact with his shin inside the six-yard area.
Isak went close to netting a dream winner on his home bow in the dying stages as the Swede connected with Elliot Anderson's inviting cross but the striker's clever flick towards goal was blocked by Andersen.
Newcastle United: Nick Pope, Kieran Trippier (c), Fabian Schär, Sven Botman, Matt Targett (Dan Burn 79), Sean Longstaff, Joe Willock, Joelinton, Miguel Almirón (Jacob Murphy 70), Ryan Fraser (Elliot Anderson 70), Alexander Isak (Chris Wood 90).
Subs not used: Karl Darlow, Javier Manquillo, Jamaal Lascelles, Jamal Lewis, Matt Ritchie.
