Another encounter which was not the most entertaining, Nuno Espirito Santo's side looked to seal victory when Raul Jimenez hammered home for his fourth goal in six games.
But Murphy had the final say, catching out Rui Patricio, to make it four successive 1-1 draws with the Magpies.
Wolves' first stalemate of 2020/21 leaves them seventh in the Premier League table.
There were flashes from Nuno's pack going forward – but just not enough. The search for a complete performance over 90 minutes goes on.
Nelson Semedo had a steady showing at right-wing-back, Pedro Neto impressed again and Jimenez, predictably, came up with a fine finish that should have won it.
Wolves, though, apart from Jimenez, are lacking a clinical edge.
The star striker took his goal wonderfully, with a thunderbolt from the edge of the area proving too hot to handle. But clear-cut chances were few and far between.
And the decent opportunities which did arrive went begging. Then, Patricio got his wall set-up all wrong.
Credit to Murphy for finding the net, but it was made too easy for him.
Six games in, Wolves are on 10 points so it is not panic stations at all and a disjointed start to the campaign was to be expected given how short their pre-season was.
Nuno, though, needs other players to step up on the goal front after the losses of Diogo Jota and Matt Doherty. That is the long and short of it.
Wolves made just the one change to the side which beat Leeds 1-0 last Monday, with Ruben Neves replacing Joao Moutinho in the middle of the park.
That meant Max Kilman – fresh from signing a new five-year contract – stayed in defence and Romain Saiss carried on out of position, at left-wing-back.
Rayan Ait-Nouri made the squad for the first time since joining from French club Angers, but fellow summer signing Vitinha was not included in the 18 for the second match running.
Newcastle, meanwhile, saw goalkeeper Karl Darlow pass a late fitness test and start between the sticks.
Wolves had started tentatively in the few games before this one, so it was refreshing to see them begin with more intent – passing it around at a high tempo – against the Magpies.
Semedo was making runs down the right flank and looking to make things happen with his pace and trickery. One of those occasions saw him cleverly tee up Jimenez, whose first-time attempt went wayward.
Daniel Podence and Neto, interestingly, were operating more as conventional wingers – Podence on the left and Neto on the right – instead of shifting about in a fluid front three as seen previously.
And they were creating half-chances against the extremely-defensive visitors. Podence forced Darlow into a sharp, low save and fizzed another shot over the crossbar after Jeff Hendrick was caught napping.
Neto then danced past a couple of black and white shirts before feeding Jimenez, who cut in from the byline and saw his left-footed strike fly beyond the far post.
Wolves were not exactly pulling Newcastle apart, but it still marked a step up going forward, largely in the first 20 minutes.
Neves regularly looked for Semedo with trademark diagonal balls, as he used to with Doherty, and regularly found him. Semedo came up with some nice touches, too, and was linking up well with Neto.
Ultimately, though, the goalless first-half trend continued. Wolves were the better side in the opening 45 and Neto was a threat, but it petered out towards the break.
The Magpies, meanwhile, were quite content to sit back and try to counter – their only shot on target coming from Allan Saint-Maximin, deflecting into the arms of Patricio.
Given the tendency to step things up after the interval, there was cause for optimism. A fantastic chance came shortly into the second period, too.
Podence surged down the left and played a precise cross to Neto, who guided his shot from near the penalty spot just off target – a fraction too high.
Neto had his head in his hands, and out of desperation, he blazed one well over from long range a minute or so later.
Wolves were trying, but it was not quite happening, and Nuno had a bit of a dilemma. The game was almost crying out for Adama Traore to be introduced – but then Podence and Neto had been the two most dangerous players in gold and black.
It was a case of whether to stick or twist and come the hour mark, Nuno firmly went for the latter as he readied not one, but two changes as Newcastle had got fairly comfortable.
Traore replaced Podence while Fernando Marcal – a lot more experienced at left-wing-back – came on for Saiss.
A spark was needed as it had all become slow and laboured, with the unadventurous Magpies aiming to hold on for a point. Wolves were having enough possession but all in front of the away side.
They briefly got in behind as the ball fell kindly to Neto. His effort, though, was blocked by Jamaal Lascelles.
Then came Jimenez's moment of magic – a pure, accurate strike to finally beat Darlow and, seemingly, seal three points for the hosts.
However, it was not to be. Patricio was left bamboozled as Murphy curled a free-kick around the wall, surprisingly beating the Portuguese at his near post. A frustrating night for Wolves.
Wolves (3-4-3): Patricio; Boly, Coady, Kilman; Semedo, Dendoncker, Neves (Moutinho, 82), Saiss (Marcal, 68); Neto, Jimenez, Podence (Traore, 68)
Subs not used: Ruddy (gk), Hoever, Ait-Nouri, Silva
Goal: Jimenez (80)
Newcastle (5-3-2): Darlow; Murphy, Schar, Lascelles (Carroll, 88), Fernandez, Lewis; Hendrick, Fraser (Joelinton, 78), Almiron; Saint-Maximin (S Longstaff, 78), Wilson
Subs not used: Gillespie (gk), Krafth, Manquillo, Hayden
Goal: Murphy (89)
Referee: Lee Mason (Bolton)