Newcastle made it ten points from 12 in the Premier League in the Black Country, as second-half goals from Fabian Schar and substitute Harvey Barnes, completed an unexpected late turnaround.
Starting positively, the Magpies controlled the first 15 minutes of the game, similar to previous games this season, but gradually took their feet off the gas, allowing the hosts' counterattacks to cause the usually solid defence to become nervy.
Returning England winger Anthony Gordon almost made the breakthrough in 24 minutes, after beating both Nelson Semedo and Yerson Mosquera on the wing, before cutting inside and striking the outside of the right post.
It was Wolves however who struck first, with another expertly executed counter attack featuring Jorgen Strand Larsen, Joao Gomes and goalscorer Mario Lemina. Larsen outpaced Dan Burn in the left channel, before crossing across the box, where Gomes cleverly let the ball run to Lemina, who had a tap-in at the back post.
Come half-time, Eddie Howe sprung the changes. Both Alexander Isak and Joelinton were taken off, with suspected injuries, while Sean Longstaff, who gave the ball away in midfield for the hosts' goal, was replaced at the interval.
On came a dynamic trio of Sandro Tonali, Joe Willock and Harvey Barnes. All three changed the game positively, with Tonali adding composure to a below-par midfield, while Willock and Barnes provided energy to the left side.
Yet again, the Magpies started well, with a strong penalty shout against Craig Dawson turned away, and Tonali going close with a clever flick.
However, the middle period of the second half was again poor, with Larsen missing two considerable chances, with one hitting the base of the post, while Matheus Cunha forced a clever near post save out of Nick Pope.
Newcastle were forced to revert to long-range shots, void of ideas, and with one Schar strike ending up in the stands, he tried again, and succeeded, albeit with great help by Wolves defender Dawson, whose deflection found the top corner of Sam Johnstone's goal.
The Toon built on the Swiss defenders' goal, and soon found another, with substitute Barnes, majestically finding the top right corner after cutting in from the left.
The Magpies now had the momentum but injuries to both Bruno Guimaraes and Lewis Hall restricted their play in the final 10 minutes.
There was a chance for either side in stoppage time, with Cunha's acrobatic effort superbly pushed away by Pope, before Barnes was slid in by Willock, with his chip ending up just the wrong side of the post.
However, the miss did not have an impact on the game, and less than two minutes later the toon were celebrating their first away Premier League win of the season.
Newcastle (4-3-3)
Nick Pope - 7
Pope's save in stoppage time will have taken the headlines, but his overall performance was mixed at Molineux. The four crucial saves he made, kept Newcastle in the game, but his distribution was poor, and looked very shaky under pressure in the first half, with a few kicks finding the stands rather than a player in maroon and blue.
Tino Livramento - 6
Asked to invert off the right side of defence, it was not the 21-year-old's finest performance. Occasionally dispossessed in the middle of the pitch, the Englishman offered very little going forward, but was solid in defence, as usual, with five tackles and eight duels won.
Fabian Schar - 7.5
Back after a three-game suspension for his red card on game week one, the Swiss defender, who was brought for a mere €4 million, once again showed his class in the West Midlands. His goal highlighted the performance, but with seven clearances and an 85% pass completion ratio, the 32-year-old rolled back the years for a vintage performance.
Dan Burn - 6.5
Outpaced by Larsen for the hosts' goal, the boy from Blyth put in another solid performance for the Magpies. With 80 touches of the ball, the most he has had all season, the centre-back completed 69 passes and lost the ball only three times.
However, he did not cover himself in glory for Lemina's goal, and the lack of pace is the only obvious weakness in his game at the moment.
Lewis Hall - 7
The 20-year-old returned to the starting 11 for the first time in the league, since the opening day, and held his own on a day where his ball-playing capabilities stood out over most.
With exactly 100 touches of the ball, Hall completed 77 passes, with the only downside of his performance coming when defending 1v1 situations, as he was dribbled past on six separate occasions.
Sean Longstaff - 5
The North-Shields-born midfielder is likely to be warming a seat on the bench very soon. With Tonali back in contention, Longstaff needed to impress and didn't.
Instead, he gave the ball away unnecessarily for Wolves' goal. Dribbled past three times and unable to complete a successful defensive action, his place in the team has come under real jeopardy.
Bruno Guimaraes - 6.5
Not at his best in the Black country today, but still ahead of most in maroon and blue. Compared to his usual number of touches, 48 represents a very quiet game, but with 86% of his passes being on target, alongside winning five duels, he once again showed his quality, drawing three fouls from the hosts' defenders.
