Chris Wood had a goal disallowed for offside by VAR in the first half as the sides went in goalless at the break.
Newcastle finally took the lead through Wood, who converted from the penalty spot with 18 minutes of normal time remaining.
And that was enough to secure a crucial win for the Magpies.
Here are our player ratings from the match...
2. Emil Krafth
A solid albeit unspectacular display on his return to the side. 6 | AFP via Getty Images
3. Fabian Schar
Gave possession away cheaply on a few occasions but remained solid to keep a clean sheet. Booked. 7 | Getty Images
4. Dan Burn
Enjoyed a comfortable first half. Had the game’s first shot on target after 52 minutes. 8 | Getty Images
6. Bruno Guimaraes
Made several incisive passes from midfield. Helped give Newcastle some cutting edge going forward. Came close to scoring on his home debut but dragged a shot just wide. Left to a deserved standing ovation. 8 | AFP via Getty Images
7. Jonjo Shelvey
Was calm and composed in possession and played some good balls forward without cutting Wolves open. 7 | Getty Images
8. Joelinton
Caught on the ball on a couple of occasions. A quiet display by his recent standards but still played a key role in playing the ball through to Chris Wood to win the penalty. 6 | Getty Images
10. Allan Saint-Maximin
Often found himself frustrated by Wolves’ organised back line. Struggled to beat his man and pose a sustained threat and his passing was wayward at times. His clever flick ultimately led to the opening goal. 6 | Getty Images
11. Chris Wood
Unlucky to have a goal chalked off for offside. Held his nerve to convert from the penalty spot. 7 | Getty Images
12. Miguel Almiron
On for Fraser 13: Did well for the disallowed goal. Was typically lively, just lacked ruthlessness going forward. 6 | Getty Images
2. Emil Krafth
A solid albeit unspectacular display on his return to the side. 6 | AFP via Getty Images
3. Fabian Schar
Gave possession away cheaply on a few occasions but remained solid to keep a clean sheet. Booked. 7 | Getty Images
4. Dan Burn
Enjoyed a comfortable first half. Had the game’s first shot on target after 52 minutes. 8 | Getty Images