The Spaniard's header from Matt Ritchie's 85th-minute corner handed the Magpies a win they barely deserved on an afternoon where they were poor for long periods before producing a late flurry.
Palace, who enjoyed the better of much of the game, ultimately paid for not making the most of their chances, the best of which fit-again winger Wilfried Zaha headed wide before the break.
The bottom-of-the-table Eagles are odds-on at 8/11 with Sky Bet for relegation. Newcastle are out at 14/1 for the drop.
Post-match reaction
Rafael Benitez admitted he would happily have taken 14 points and a place in the top six after Newcastle's first nine games back in the Premier League.
Asked if he would have settled for the club's current position, he replied: "Yes, it could be.
"Obviously, we have come from the Championship and we didn't sign too many players, so if you were telling me that after September 1, I would have said to you, 'It's fine'.
"We have to keep working and credit to our players because they are doing really well."
Palace boss Roy Hodgson was disappointed to have come away empty-handed, but remains convinced he can drag the Eagles out of trouble.
He said: "Why should I not believe that? There are 31 games to go. We have beaten the champions and we have come here today to St James' Park against a Newcastle team doing very well and once again - in my opinion - matched them and even - again, in my opinion - were the stronger team through large periods of the game, so why should I not have belief?
"I shall stop believing when the number of points that we are behind doesn't match the number of games that are left.
"That's not going to happen in October. That could happen some time in March, April, I would think, at the earliest, so there's a lot of work to do before then."
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