Relegation remains a mathematical possibility, but appears only a distant threat after Roy Hodgson's side moved 11 points clear, four ahead of their hosts.
Magpies boss Rafael Benitez revealed in the build-up to the match that he was waiting for confirmation over his future at the club, but may face a further delay until the Magpies can secure their own top-flight status.
Both sides had a goal disallowed in the first half, with Salomon Rondon and James Tomkins the frustrated parties, though replays showed the officials were right in both instances.
With Newcastle having won their last five in a row at home, hopes will have been high among their fans for a late winner, but it did not go the way they expected, with an injury to Florian Lejeune giving further cause for concern.
Vicente Guaita breathed a sigh of relief after spilling a cross into the path of Rondon, whose goal was ruled out for offside.
Matt Ritchie called the goalkeeper into action again at the end of a swift counter-attack as the hosts continued to pose the greater threat.
It was not all one-way traffic, though, and some tricky wing play from Wilfried Zaha threatened to unpick the home defence, who eventually dealt with the cross as James McArthur was lurking.
There was still time for Guaita to repel a low Rondon effort and Palace to have a goal of their own chalked off with McArthur deemed active in an offside position when Tomkins stroked home.
The hosts lost Lejeune, who underwent knee surgery last August, to what looked to be a serious injury in a closing 30 minutes that took another turn for the worse late on.
DeAndre Yedlin's foul on Zaha allowed Milivojevic to net his 10th penalty of the season with Palace's first shot on target.
What does it mean? Safety in sight for Eagles
It has been the primary objective for both these sides to stay in the Premier League, and Cardiff City's loss at Manchester City in midweek means this was a huge win for Palace, and a defeat that leaves Newcastle in much the same position.
Rondon a handful
He did not score and perhaps he should have, but Rondon was a persistent threat for Newcastle and you have to admire forwards who keep getting in the right positions, even when the end product is lacking. He more than anyone will feel hard done by to end up on the losing team.
Guaita not convincing
There was a nerviness about Palace keeper Guaita that seemed to transfer to his defence at times. He flapped and fumbled, but escaped with a clean sheet nonetheless.
Key Opta Facts:
- Crystal Palace have won 59 per cents of their Premier League points away from home this season (23/39), the highest such ratio in the division.
- Newcastle are winless in all 11 of their Premier League games against London sides this season, drawing two and losing nine.
- Palace won despite having just three shots on goal in this match – no side has won a Premier League game with fewer attempts this season (Burnley versus Cardiff in September also three).
- Luka Milivojevic has scored 10 Premier League penalties for Palace this season – only Andrew Johnson in 2004-05 (11, also with Palace) has scored more in a single campaign in the competition.
- Milivojevic has scored 13 per cent of all the penalty goals in the Premier League this season (10/76).
Newcastle head to Leicester City for a Friday night game, while Palace will aim to complete the most unlikely of league doubles when they host Manchester City two days later.