Miguel Almiron sent St James' Park into raptures when his curling effort nestled into the top-left corner of the net on 32 minutes.
The victory for the hosts moved them up to 11th in the table and 15 points clear of the relegation zone.
Story of the game
Newcastle – who tonight were being watched by their chairman Yasir Al-Rumayyan for the first time since their embarrassing loss to Cambridge United – were unchanged from the side that beat Leicester City with the last kick of the game on here on Sunday.
It meant that the man who came up with the assist for Bruno Guimarães' dramatic winner, Joe Willock, found himself among the substitutes once again.
The Eagles on the other hand made five changes after they lost at Wembley Stadium to Chelsea in an FA Cup semi-final at the weekend, with Conor Gallagher being the standout returnee to Patrick Vieira's starting lineup.
Still full of confidence from their last-gasp winner, Newcastle looked to start quick and had the visitors' backline sweating after just 10 minutes, with two close chances being manufactured by them early on in his tie.
With seven minutes on the clock, some well-worked give-and-go play from Guimarães and Joelinton the edge of the area saw the ball shifted right to Miguel Almiron – but England international Marc Guehi got a vital block on the Paraguayan's effort.
The Magpies No.7 was at the heart of the second chance too after his tackle set Allan Saint-Maximin – who was playing like a man who seemed to really want to impress his former manager in Vieira – drove at the Palace defence before angling to shoot after working space, but his effort was tame and easily saved by Vicente Guaita.
Palace broke with pace, and managed to get two-on-one, but as the French forward looked to play the ball to a wide-open Michael Olise on the right-hand flank, Matt Targett excellently stopped the move in its tracks with a crucial interception.
Chris Wood – who hasn't exactly had the rosiest time in front of goal since his £25 million move to Tyneside in January – had his blushes spared by the offside flag after found himself through on goal and managed to push his effort wide of the goal.
But after over half-an-hour of knocking on the door, the hosts got themselves in front, and to say it was a peach of a goal was an understatement.
In his own half Guimarães knocked the ball over-the-top of the Palace high defence line and set Miguel Almiron away to sprint with the ball.
And sprint is what he certainly did.
The 28-year-old darted for goal and got the right side of Guehi before shifting onto his favoured left foot and curling his effort perfectly into the top-left corner of the net – before wheeling off in celebration. Topless I should add.
It seemed that Almiron may have turned into Lionel Messi overnight – a statement that was proving to be more and more correct when he flicked the ball over a Palace players' head before volleying at Guaita.
But his effort was caught by the Spaniard, signalling the last chance of a half utterly dominated by the hosts.
Palace improve, but Newcastle hang on
Picking up from where they left off prior to the interval, Newcastle had a big opportunity to double their lead go begging when Joelinton was unable to steer his header on goal after Targett picked him out from a free-kick.
Before you knew it, a quarter of the half had passed with barely any chances created by either side.
It was, however, Palace's best spell of the game, but with the visitors still were struggling to have any presence offensively. They brought on Jean-Philippe Mateta to try and change that on the hour mark.
You slowly started to feel sat watching the game that the momentum was shifting towards Vieira's side – and they came inches away from equalising on 65 minutes.
After a bit of pinball on the edge of the penalty area the ball fell into the path of Edouard who managed to play the ball through to Wilfried Zaha, whose side footed effort clipped the left-hand post.
The Eagles kept coming, though.
This time Jordan Ayew – who was introduced into the match before half-time in place of Olise after just 40 minutes – worked space down the right-wing and managed to cross into the path of Mateta, but the striker's header went well over Martin Dubravka's goal.
As we went into the final 10 minutes of the game, it was clear that Newcastle were looking to shut up shop.
They sat deep – something their head coach calls 'survival mode' – survived a late scare when Zaha cut in on his right and shot narrowly over the crossbar in the 93rd minute, but managed to get over the line and reach the precious 40-point mark.
Their win moves them up to 11th in the table, three points ahead of their opponents this evening.
Newcastle: Dubravka; Krafth, Schar, Burn, Targett; Guimarães, Shelvey, Joelinton; Almiron, Wood, Saint-Maximin. (4-3-3)
Crystal Palace: Guaita; Clyne, Andersen, Guehi, Mitchell; Kouyate, Schlupp; Olise, Gallagher, Zaha; Edouard. (4-2-3-1)