Building on a sublime second-half at Southampton, Nuno Espirito Santo's pack had a bit of luck on their side to come out on top at Molineux and make it back-to-back wins.
Adama Traore's long-range fizzer smacked the crossbar and back off keeper Meslier before finding the back of the net.
Wolves had Rui Patricio to thank for some top saves along the way as well, but they displayed both quality and a heartening work-rate to complete the double over Marcelo Bielsa's men.
They have also gone above Leeds in the table, into 11th.
There were a lot of positives for Nuno to take from this win, and supporters can go into the weekend with smiles on their faces.
The willingness to press, get bodies up the pitch and, most importantly, get shots off was much more like it from Wolves.
So often this season they have been so reserved, but there was none of that against Leeds.
The visitors have developed a reputation for taking risks and looking to play attractive, attacking football, and Wolves fought fire with fire.
Lady luck was on their side with the goal, but they earned that good fortune as that Traore attempt was not a one-off. Far from it.
It was one of many strikes from distance and if you don't buy a ticket, well, you won't win the raffle.
Patricio was on his mettle to keep the visitors at bay and claimed a well-deserved clean sheet – not only with his saves, but his calm claims from crosses which took the pressure off time after time.
Seeing Fernando Marcal, who has been blighted by injuries throughout his time at Wolves so far, go off with yet another problem was a concern.
But on the whole, Wolves can look back on this as a top night's work.
A rare occurrence given the number of injuries and indifferent results this season, Nuno went with the same XI for the second game running. The nine-man bench was also unchanged.
Leeds, meanwhile, brought former Albion attacker Tyler Roberts in for Ezgjan Alioski, with former Molineux man Helder Costa among the substitutes.
Trying to build consistency and have a brighter end to what has been a difficult campaign on the whole, it was nice to see Wolves stick to their guns.
Traore and Pedro Neto were playing as inverted wingers – after it worked a treat in the second half at Southampton – and the latter had the game's first meaningful effort.
Given time and space to have a go from 30 yards, his lovely, left-footed curler forced Meslier into a fine, flying save.
The Portuguese kept having shots from long range, too. Another one with his left was comfortably gathered by Meslier, and then one with his right sailed wide.
But the intent was encouraging. After all, Wolves having so many attempts in the first half is not exactly standard practice.
Leeds, though, were also having their moments. Raphinha's inviting free-kick was met by Liam Cooper, who could only head into the grateful hands of Patricio. Patrick Bamford was denied by a decent Leander Dendoncker block, too.
Wolves, in fairness, were not afraid to mix it up against the high-energy, bold visitors.
Another instalment in a series of end-to-end sequences saw Matheusz Klich – seemingly aiming to cross the ball across the face of goal – almost catch out Patricio at his near post, clipping the inside of the woodwork, before Pascal Struijk's drive was kept out by the Portuguese.
Nuno's lot then raced up the pitch on the counter-attack as Neto played a clever reverse pass to Nelson Semedo, who really should have scored.
Putting it at a nice height for Meslier to save pretty easily, unfortunately, it was the finish of a full-back. The ex-Barcelona man, though, credit to him, kept making his presence felt in the final third – Meslier stopping another shot from an acute angle.
The final touch was not there, for either team, but Wolves' attitude and application made for a progressive, positive half. There was no element of sitting back. They were entertaining to watch.
Unsurprisingly, no changes were made for the start of the second period – both bosses happy with what they saw.
Nuno's charges were the ones applying the pressure shortly after the restart. A prolonged spell of possession resulted in Ruben Neves firing high and wide from distance.
Neto then went for a goal after Jack Harrison was tackled, but Jose, who was free in the area, was left frustrated as the winger's strike sailed over.
On the hour mark, Wolves made their first substitution. Jonny Castro Otto – gradually working his way to full fitness having spent several months out with a severe knee injury – was replaced by Marcal.
And soon after, getting the rub of the green, the home side went ahead.
Traore's right-footed rocket cannoned off the bar, bounced off Meslier's back and rolled over the line.
Hugely unfortunate for Leeds, and the goalkeeper especially, but it was a reward for Wolves' endeavour and more forward-thinking approach.
Bielsa's outfit, though, still needed to be monitored very closely. Cooper, in particular, continued to look a threat from set-pieces.
A heart-in-mouth moment came as Bamford, sharply latching onto a through-ball, fired beyond Patricio but saw the assistant's flag raised against him – VAR confirming the striker was marginally offside.
Injury-plagued Marcal, having not long replaced Otto, was then forced off with another knock, dampening his 32nd birthday.
Rayan Ait-Nouri entered the fray as the Brazilian limped down the tunnel, and Patricio had to keep out both Costa and Raphinha late on.
Ultimately, though, Wolves were able to hold on for a hard-fought, uplifting victory.
Wolves (3-4-3): Patricio; Dendoncker, Coady, Saiss; Semedo, Moutinho, Neves, Otto (Marcal, 60) (Ait-Nouri, 82); Neto, Jose (Silva, 87), Traore
Subs not used: Ruddy (gk), Hoever, Kilman, Otasowie, Vitinha, Gibbs-White,
Goal: Meslier OG (64)
Leeds (4-2-3-1) Meslier; Ayling, Cooper, Struijk, Dallas; Shackleton (Hernandez, 66), Klich (Alioski, 81); Raphinha, Roberts, Harrison (Costa, 81); Bamford
Subs not used: Casilla (gk), Llorente, Davis, Jenkins, Huggins, Gelhardt
Referee: David Coote (Nottinghamshire)