Meetings between the two sides in the Black Country have more often than not seen the spoils shared in recent years, and this one looked to be heading for another draw.
Eddie Howe's side fell behind in the first half when a swift Wolves counter-attack ended in Mario Lemina sweeping home but Fabian Schär levelled in the second period with a trademark strike from range.
But with just ten minutes remaining, substitute Harvey Barnes turned the game on its head with a stunning goal worthy of winning any match.
It was a strong finish from the Magpies that propelled them to victory but, wearing their navy and burgundy away kit for the first time, they'd started well too.
In the seventh minute Alexander Isak - who had already seen a shot on the turn blocked by Craig Dawson - picked up the ball in a deep area and threaded a pass through to Jacob Murphy, whose first-time effort was pushed over the bar by Sam Johnstone.
Then Anthony Gordon was desperately unlucky to see his shot hit the far post after a brilliant run on the left had bamboozled Nelson Semedo and Yerson Mosquera and taken him into the box.
However, Wolves then wrestled the initiative from United and, after Schär blocked well from Semedo, Jean-Ricner Bellegarde fired over after some impressive approach play.
In the 36th minute, a Newcastle attack broke down allowing the hosts to counter and when Jorgen Strand Larsen crossed from the right, Joao Gomes cleverly stepped over the ball and Lemina was able to convert from close range.
Nick Pope needed to beat away a Rayan Ait-Nouri shot before the break and Eddie Howe made a triple-substitution at half time, with Barnes, Joe Willock and Sandro Tonali entering the fray in place of Isak, Joelinton and Sean Longstaff.
Within two minutes of the restart, Bruno Guimarães had a shot from the edge of the area pushed away by Johnstone and the pressure continued when Schär shot over following a goalmouth scramble where the visitors appealed for a penalty when the ball hit the hand of Craig Dawson.
Wolves fired a warning shot in the 53rd minute when Strand Larsen struck the base of a post, but on the hour mark Tonali had a flicked effort saved by Johnstone.
Pope kept out a Strand Larsen header, then at the other end a looping header from Dan Burn was just too high.
In the 68th minute, Matheus Cunha was denied by a combination of Pope and post, and seven minutes later that became all the more crucial as Schär levelled.
The defender was recalled after serving a three-game suspension for his opening-day red card and tried his luck from 25 yards, with his piledriver skimming Dawson's head on its way into the top corner.
If that was a good goal, Barnes' was even better five minutes later. The substitute recieved the ball from Willock, cut inside and curled a right-footed strike beyond Johnstone.
Tonali then saw a shot saved and both sides had an opportunity in eight minutes of stoppage time.
First, Pope flew to his right to thwart Cunha, then Barnes dinked wide with almost the last kick. But the former Leicester winger had already done enough to seal all three points for the Magpies as Howe's brave half-time changes paid off.
