The New Zealand striker was on target 18 minutes from time, with his second goal for the Magpies since his £25 million January transfer window move from Burnley, helping Newcastle move 10 points clear of the relegation zone with seven games to play.
Newcastle kicked off at St James’ Park on the back of a 5-1 loss away to Tottenham Hotspur, their third successive league defeat.
But they are now on the brink of being assured of their place in the top flight next season, which will be a huge boost to the Saudi-backed consortium who bought the northeast club in October.
For Wolves, defeat was a blow to their hopes of European football, with the visitors still two points adrift of sixth-placed West Ham having played two more games than the London club.
Bruno Guimaraes was handed a first start at St James’ Park by Newcastle manager Eddie Howe as the Brazil international and Emil Krafth replaced the injured Joe Willock and Javier Manquillo in the team which started last weekend’s loss at Spurs.
Wolves manager Bruno Lage also made two changes, with Hwang Hee-chan and Luke Cundle coming in for Leander Dendoncker and Daniel Podence.
Newcastle thought they had broken the deadlock in the 24th minute when Wood shot home after Guimaraes had exchanged passes with substitute Miguel Almiron and crossed, only for his effort to be ruled out for offside following a VAR review.
Although Newcastle had the better of the game, Wolves had chances in an increasingly open second half.
Hwang had a close range effort blocked and Joao Moutinho drilled a cross across the face of goal.
Newcastle’s Allan Saint-Maximin had a frustrating match, shooting high over the bar in the 64th minute before the Frenchman failed to find Wood at the far post moments later .
The Magpies, however, finally went ahead 18 minutes from time when Wood ran onto Joelinton’s pass only to be upended by Jose Sa as the Wolves goalkeeper rushed off his line.
Referee Peter Bankes pointed to the spot and, following a VAR check, the penalty stood.
Wood took the spot-kick himself, calmly sending Sa the wrong way, to the delight of the majority of crowd of over 52,000.