Star man Raul Jimenez won it as his shot from the edge of the box took a huge nick off Kalvin Phillips, much to the relief of Nuno Espirito Santo.
His lot were well below par in the first period, but they also had a Romain Saiss strike chalked off as they looked an entirely different side after the interval.
Wolves, five games into the 2020/21 campaign, have risen to sixth in the Premier League table.
They are still searching for a complete performance over 90 minutes and they got the rub of the green – but it is another win.
It would be lovely to see Wolves put it together in both halves instead of just one, of course.
The main thing, though, is that they are still picking up results in what is a bit of a transitional period. Fingers crossed, the victories will become more stylish as the season progresses.
While ability was not on show all night, character came through from Nuno's charges.
After all, the first 45 was not enjoyable for anyone of a gold and black persuasion – passes were being misplaced and Leeds, in truth, were having their way with Wolves.
But in the second, they had the ball in the net twice, with the first from Saiss ruled out for offside before Jimenez found the net via the head of Phillips.
It was fortunate, no doubt, but you also make your own luck and the work from Jimenez to create the opportunity was top-drawer.
Wolves are far from the finished article, but a win is a win.
Nuno, quite surprisingly, only made one change to the side which beat Fulham 1-0 before the international break.
That meant Saiss again filled in at left-wing-back, with Max Kilman keeping his place in the back three.
Joao Moutinho was the one who came in, for Ruben Neves, while summer signings Vitinha and Rayan Ait-Nouri did not make the squad.
Leeds, meanwhile, had former Molineux man Helder Costa in from the off, and they also had to make a last-minute change to the starting XI as Pascal Struijk replaced Liam Cooper at centre-half.
That late switch had the potential to cause unrest for the hosts, but they started far sharper than Wolves.
Costa was the main threat, having a lot of joy against Saiss, and Patrick Bamford even headed in from a corner routine which caught Nuno's pack completely cold – luckily, the striker being a few yards offside.
A let-off, but the general theme continued, with Marcelo Bielsa's charges having much more zip about their play than Nuno's pack.
Costa flashed one wide following a swift counter-attack while Wolves were anxious in possession amid a trademark high press from Leeds, putting too much weight on their passes.
Half an hour had passed and a significant attack had not been forged. The home side were dictating play – wave after wave.
As the interval approached, Wolves finally mustered something of note. Pedro Neto won their first corner, 34 minutes in, through some fancy footwork and from it, Moutinho played it low to Jimenez, who flicked the ball over the bar.
Not a sitter, but the Mexican would have been disappointed not to hit the target. A swift move also saw Daniel Podence, after a clever cut-back from Saiss, sting the palms of Illan Meslier on the stroke of half time.
On the whole, though, the first period was dominated by Leeds – much more imaginative and threatening.
Rodrigo, who Nuno managed at Valencia, saw a shot fly straight into the hands of Rui Patricio as Costa continued to look lively.
Wolves certainly needed to step things up as, honestly, it was flat and dull. And they so nearly made the perfect start to the second half.
A sense of urgency, along with quality, emerged as Conor Coady played a raking crossfield pass to Podence.
The Portuguese then did brilliantly to find space and play it to the far post for Saiss, who finished sublimely – only, and agonisingly so, to be ruled out for an offside against Podence after a lengthy VAR review.
Disappointing to see such a stylish goal chalked off, but Wolves continued to operate with far greater vigour.
A long-range drive from Podence forced Meslier into another sharp save while Jimenez just lost his footing as he tried to wriggle free in the box.
They were putting the pressure on, showing glimpses of the old Wolves. In an attempt to strike more fear into Leeds too, Adama Traore – on the cusp of a new contract – entered the fray in place of Podence.
And, with a big slice of luck, the goal came. After a long punt upfield from Kilman, Jimenez did superbly to dribble inside and check back onto his right foot before his strike took a massive deflection off Phillips and left Meslier helpless.
Pretty lucky, but Wolves gladly took it. Neves and Fernando Marcal came on to shore things up for six minutes of stoppage time and, overall, it was not pretty. Ultimately, though, it is another three points in the bag.
Leeds (4-4-1-1): Meslier; Ayling, Koch, Struijk (Hernandez, 75), Dallas; Costa (Poveda, 71), Phillips, Klich, Harrison (Raphinha, 82); Rodrigo; Bamford
Subs not used: Casilla (gk), Alioski, Shackleton, Roberts
Wolves (3-4-1-2): Patricio; Boly, Coady, Saiss; Semedo, Dendoncker, Moutinho (Neves, 82), Saiss; Neto (Marcal, 89); Jimenez, Podence (Traore, 65)
Subs not used: Ruddy (gk), Hoever, Otasowie, Silva
Goal: Jimenez (70)
Referee: David Coote (Nottinghamshire)