Danny Ings scored for the fourth successive game to end Southampton’s three-match losing run in the Premier League.
It is the first time in Ings’ career that he has reeled off this many scoring games in a row, with his strike here - which punished poor Wolves defending - giving his side a 1-0 lead early in the second half.
Mexico striker Raul Jimenez levelled from the spot, to make up for having two efforts ruled out by VAR in the first half, meaning Wolves’ unbeaten run stretches to six in all competitions.
The VAR denials were frustrating for Wolves - spoiling celebrations - but the officials could not be accused of making mistakes on either call.
Wolves had kept three clean sheets in succession before this match but a blunder from the shaky Jesus Vallejo then a misjudgement by Conor Coady allowed Ings to pounce.
While £15 million attacker Che Adams was on the bench, left waiting for a goal, £20m man Ings is benefiting from his fitness and his run of regular starts.
Southampton academy product Ings, 27, is looking increasingly at home with his new permanent employers and showing the form that earned the former Liverpool striker an England call-up.
Wolves started positively with Joao Moutinho striking over one chance from 25 yards, but Southampton were generally restricting them diligently.
The visitors also began threatening on the counter-attack - as Wolves struggled on their own right flank - with lively Nathan Redmond and Ings both having shots blocked by alert Wolves defending.
Jimenez was frustrated for the first time in the 29th minute when he controlled and struck in, but VAR ruled his effort out for a handball while bringing the ball down, and he was booked as a result. The ball struck an arm so the decision to rule the goal out was justifiable, but the caution was harsh.
The Mexican was denied again, just before half-time, after he had tapped in, inside the six-yard box on the rebound after Italy-capped forward Patrick Cutrone had a shot saved. This time, VAR denied Wolves for a marginal offside against Cutrone when the former AC Milan striker received the ball.
Southampton spurned a chance early in the second half when Ings shot at Rui Patricio after Vallejo had given the ball away.
Ings quickly made amends though after more poor Wolves defending, with Vallejo again involved. Vallejo had sliced a clearance forward, allowing Pierre-Emile Hojbjerg to head the ball back into a dangerous area. Wolves captain Coady made a mess of clearing it and Ings took advantage, striking in.
Wolves bit back quickly, however, winning a penalty when substitute Matt Doherty tumbled following Hojbjerg’s challenge. Jimenez was cool from the spot, slotting in to the right of goalkeeper Angus Gunn.
Nuno’s men carried on imposing themselves after that, with substitute Diogo Jota causing problems, but James Ward-Prowse almost forced a Southampton winner as his free-kick was saved by Patricio.