The striker's penalty fired Nuno Espirito Santo's men to an unconvincing victory as they moved into second in Group K.
Diogo Jota was sent off late on after two quickfire yellow cards but they survived to sit a point behind group leaders Braga.
The game was initially due to be played behind closed doors after Bratislava were sanctioned for racist chants and a banner from their fans in the Europa League play-off game against PAOK in August.
It had the atmosphere of a pop concert, especially with a pre-match light show for the 20,333 fans – most of them under 14 years of age.
And if Wolves were expecting it to be child's play in front of thousands of kids they were proved wrong after falling behind after 11 minutes.
Sporar was picked out by a brilliant ball from Rabiu Ibrahim which split the Wolves backline.
It was another costly mistake from Coady, whose error gifted Danny Ings a goal in Saturday's 1-1 draw with Southampton.
Gibbs-White should have levelled three minutes into the second half but he scuffed his eight-yard shot at Greif.
The impressive Sporar then unleashed a warning shot which Patricio tipped over before the game turned in five second-half minutes.
There was little danger when Saiss collected a loose pass in midfield but Bratislava allowed him to advance.
The midfielder was given time to shoot and his 30-yard effort took a deflection to wrong-foot Greif, who could not keep it out.
Then, with Wolves' tails up, Vernon De Marco pushed Jimenez in the back as he tried to reach Vinagre's cross and the striker picked himself up to stroke in the spot-kick.
It knocked what courage Bratislava had left and, aside from a miscued Sporar header, they never went close to levelling.
Yet Wolves still had to negotiate the final few minutes with 10 men after Jota's mindless red card.