An own goal from home defender Silvio Manuel Pereira gave the Whites victory at Molineux and they survived a late scare to avoid a second successive late dropping of two points.
But the clean sheet pleased Leeds boss Monk who felt his side deserved to bring back all three points from the Midlands.
He said: “Three points and a clean sheet - you have got to be happy.
“We are really competitive now.
“Overall our character shone through today and we got the deserved three points.
“I think we saw it out quite comfortably.
“I think that it was an excellent performance. A really gritty typical Championship game where you have to dig in.
“We showed that side of it and I think that part of control and bit of football that we want to put on the pitch was there in patches today.
“You can’t always have it your own way, the Championship doesn’t allow you that.
“We are going in the right direction. You can see it. The group are very good together. They were determined and got the three points.
“We need to be a bit more clever with the final decisions but that will come. They are young players and young players do not always make the right decisions, but we are getting better as a team and when it doesn’t go our way we show character.
“They are growing into it and it is my job to keep improving them and pushing them.”
Monk made one change from the team that drew at home to Wigan in midweek with Ronaldo Vieira surprisingly chosen to fill the boots of the injured Pablo Hernandez who missed the trip with a dead leg.
Leeds started sluggishly and had to survive early pressure from Wolves before they were aggrieved not to be given a penalty as Kyle Bartley went down in the box.
Vieira curled a shot well wide and United were grateful to Pontus Jansson and Rob Green for surviving when a poor back-header by Eunan O’Kane was pounced on by Nouha Dicko.
Joao Teixeira hit an effort over from the resulting corner and Jansson again came up with a great piece of defending to prevent Nouha Dicko from pulling the trigger inside the box.
Teixeira looked the Wolves danger man and he curled a 24th minute shot narrowly wide.
Teixeira then turned provider for Helder Costa, who saw his drive from 25 yards dip just over.
Leeds, however, came closest to a first half goal as Bartley’s long ball sent winger Hadi Sacko racing away and his shot beat the home keeper only to unluckily bounce off the crossbar.
Within a minute the Whites were defending again as Jon Dadi Bodvarsson had a shot blocked and Teixeira’s follow-up was saved at point blank range by Rob Green.
Leeds hit back as a Kemar Roofe sent a header just wide, but it stayed goalless to half-time.
United started the second half well with Kalvin Phillips hitting a shot wide and another big penalty shout coming as Chris Wood appeared to be brought down by Danny Batth.
Wolves went close when Helder Costa hit a shot just over, but Leeds were quickly on attack again with Carl Ikeme forced to produced a save to tip a rising shot from Wood wide.
United finally broke the deadlock in the 71st minute when Sacko took the ball off home full-back Matt Doherty before sending in a low cross for Roofe in the middle. Before the Whites player could reach the ball, Silvio got there first only to inadvertently put the ball into his own net.
Roofe was soon in the thick of the action again when shooting over.
Jansson blocked a shot from Romain Saiss as Wolves looked to hit back, but it was Leeds who should have scored again only for Wood to hit a powerful half-volley over from 10 yards out.
It was the hosts who were disappointed not to score in injury-time when the ball fell invitingly for Costa in the box, but under a desperate challenge from Charlie Taylor he blazed his shot over.
Leeds survived their late scare, unlike in midweek, and had three valuable points to take them to within three of the play-off places.
Wolverhampton Wanderers 0
Leeds United 1
(Silvio og 71)
Saturday, October 22, 2016
Wolves: Ikeme, Doherty (Coady 76), Silvio, Edwards, Batth, Dicko (Cavaleiro 62), Costa, Bodvarsson, Teixeira (John 76), Saiss, Hause.
Leeds: Green, Ayling, Bartley, Jansson, Taylor, Phillips, O’Kane, Sacko (Cooper 88), Vieira (Mowatt 86), Roofe, Wood (Doukara 90).
Referee: Stuart Attwell.