The result means the Premier League side now have a great chance of qualifying for the knockout stages of the competition.
Wolves, who included Max Kilman and teenage midfielder Morgan Gibbs-White in their starting line-up in Slovakia, fell behind in the 11th minute when Andraz Sporar scored.
The Slovenia international held off Conor Coady’s challenge and beat Rui Patricio with a deflected shot after Rabiu Ibrahim had set him up with a fine throughball.
Nuno Espirito Santo’s side went close to equalising when Morgan Gibbs-White’s 20-yard effort flew just wide while at the other end Mohammed Rharsalla’s shot from the edge of the box was deflected over the bar.
In the second half, after Rui Patricio had done well to save another effort by Sporar, the visitors equalised in the 58th minute when Romain Saiss’ ambitious long-range effort deceived Slovan goalkeeper Dominik Greif who somehow allowed the ball to fly through his hands.
The goal lifted Wolves and they took the lead from the penalty spot in the 63rd minute after the Argentinian defender Vernon De Marco had fouled Raul Jimenez who got up to convert the spot-kick himself.
Slovan pressed for an equaliser but Rui Patricio made another smart stop to deny Sporar.
Wolves had to play for the last few minutes with 10 men as Diogo Jota was sent off after fouling Vasil Bozhikov and picking up a second booking but the visitors held on to secure a welcome victory.