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...
1. Martin Dubravka
Made a very good save to deny Silva late on. 7
2. Emil Krafth
A solid albeit unspectacular display on his return to the side. 6
3. Fabian Schar
Gave possession away cheaply on a few occasions but remained solid to keep a clean sheet. Booked. 7
4. Dan Burn
Enjoyed a comfortable first half. Had the game’s first shot on target after 52 minutes. 8