Wolves went into the game in Yorkshire on the back of a poor performance at Fulham, but Nuno's team looked confident from the opening whistle and created their first opportunity through Leo Bonatini, who saw a shot deflected wide of the post.
Towards the end of the opening quarter, Ivan Cavaleiro saw a well-struck effort saved by Bailey Peacock-Farrell - who was making his first appearance of the season - but Wolves should have taken the lead moments later when Diogo Jota missed his kick from three yards out.
Jota was also denied by a block by Peacock-Farrell after the ball had been diverted into his path, but Wolves finally had their opening goal when Saiss headed the ball into the bottom corner after meeting Barry Douglas's inswinging corner.
Leeds briefly got themselves organised after a stoppage in play for an injury to Liam Cooper, but Bonatini soon missed another chance for Wolves, with the striker dinking the ball too close to Peacock-Farrell after being played in by Alfred N'Diaye.
However, a minute before the break, Wolves deservedly doubled their advantage when Boly was able to head into an empty net after Danny Batth had struck the crossbar from Douglas's corner.
After the restart, Wolves picked up where they had left off but chances were not coming as regularly as in the first half and it was Leeds who got the first effort away with Gaetano Berardi firing just off target from 30 yards.
Wolves still remained in full control of the match, however, and the West Midlands outfit came agonisingly close to a third when Jota rattled the underside of the crossbar having cut inside onto his right foot inside the penalty area.
Nuno's first switch saw Afobe introduced in place of Bonatini and the Bournemouth loanee - who has just started his second spell at Wolves - did not take long to get on the scoresheet for the first time since his January arrival.
Jota sent the ball over the top of the Leeds defence and Afobe - sensing that Peacock-Farrell was running out of goal - fired a volley over the goalkeeper and into the top corner of the net from 25 yards.
The final 15 minutes passed by without incident, and Wolves can now turn their attention to their important clash with West Midlands rivals Aston Villa on Saturday evening.
LEEDS UNITED (4-2-3-1): Peacock-Farrell; Anita, Jansson, Cooper (Pennington, 36'), Berardi; Phillips, Forshaw; Sacko (Hernandez, 46'), Saiz, Dallas; Lasogga (Ekuban, 73')
WOLVERHAMPTON WANDERERS (3-4-3) Ruddy; Batth, Coady, Boly; Doherty, N'Diaye, Saiss, Douglas; Cavaleiro (Gibbs-White, 86'), Jota (Costa 75'), Bonatini (Afobe, 70')