Entering their third successive top-flight campaign, Leeds have won their first opening match since their return after striker Patrick Bamford crossed the ball to Brenden Aaronson, who seemed to have finished it off from close range.
However, closer checks showed it was Wolves' Ait-Nouri who bundled ball over the line in the 74th minute, not the Leeds winger who was making his debut.
Leeds boss Marsch, who took over from Marcelo Bielsa in February, handed league debuts to four new signings, as defender Rasmus Kristensen and midfielders Tyler Adams and Marc Roca also made the lineup.
Despite losing key players Raphinha and Kalvin Phillips in the transfer window, Leeds rose to the occasion and ensured that Marsch has now won his opening league match in five of his last six campaigns.
Wolves, who were without their two forwards Raul Jimenez and Adama Traore due to injury, took an early lead through Daniel Podence in the sixth minute when his shot took a bounce and found its way into the net over Leeds goalkeeper Illan Meslier.
The hosts equalised in the 24th minute after Rodrigo Moreno, who scored five goals in their five pre-season friendlies, received the ball inside the box and tapped it in low inside the near post under the diving goalkeeper Jose Sa.
Both teams had good chances to make it 2-1 just before halftime.
However, Leeds strikers Rodrigo and Bamford were both a fraction of a second late to reach Jack Harrison's sublime cross into the area, while Leander Dendoncker wasted Hwang Hee-chan's spectacular back-heel pass as his low slot was saved by Meslier.
In the 68th minute, Wolves' Ait-Nouri was approaching another good chance but was brilliantly stopped by Kristensen who prevented a one-on-one scoring situation in the home side's area.