The Saints led through a superb Danny Ings volley, having completely dominated the first 45 minutes.
Brilliant Neto is Wolves' shining light
In a season that has proved underwhelming for Wolves, one of very few positives has been the emergence of Pedro Neto.
The 20-year-old picked up his fifth goal of the season with a brilliant match-winner at St. Mary's, as he turned Jannik Vestergaard inside and out before curling the ball past Alex McCarthy from a tight angle.
Neto and Adama Traore were thorns in Southampton's side for the entire second half, after being restricted by Wolves' game plan in the first. Both wide men attacked their full-backs in a way Wolves fans haven't seen for a while and always looked to drive forward after half-time.
For Neto, his ninth direct goal involvement of the season means he now has the most goals and assists of any under 21 Premier League player this campaign, ahead of the likes of Phil Foden and Bukayo Saka.
If Wolves' league position doesn't improve, keeping hold of a player who seems destined for greatness will be a tall order.
Patricio silences critics with superb display
After going just over three months without a clean sheet before last weekend's goalless draw against Leicester, Rui Patricio has come in for some criticism from some fans and sections of the local media.
The Portuguese keeper silenced that criticism with a brilliant display on the South Coast. Patricio saved brilliantly from Nathan Redmond in the first-half while Wolves were under the cosh, before denying James Ward-Prowse and then Che Adams in quick succession after his side had taken the lead.
Unlike a typical Patricio performance the Wolves keeper was also commanding, as he claimed a late Southampton corner to ease the pressure on his backline.
With John Ruddy's shaky performance against the same opposition in midweek, any debates about Wolves' number 11's position have rightly been silenced.
Why couldn't this have happened three days ago?
While Wolves fans will be happy with the three points, frustration is still running high about Nuno's team selection in the FA Cup on Thursday.
Today's three points have risen Wolves to 12th in the Premier League table, but the Molineux faithful believe that the fifth round tie three days ago heralded a greater prize. With a win on Thursday, Wolves would have been a victory against Championship side Bournemouth away from another trip to Wembley in April.
Although Wolves have picked up a rare away win, the questions over why Nuno started Morgan Gibbs-White and Vitinha over Neto and Traore have only become bigger. In what looks set to be a mid-table campaign, Wanderers should have gone all out to win their first piece of silverware in 41 years.
With every place higher in the league offering millions to the club's hierarchy, the Wolves board won't be complaining. The fans, however, will be wishing Nuno had his priorities the other way round.