The sports court of the German Football Association (DFB) delivered their verdict on Monday, declaring Munster as 2-0 victors after Wolfsburg.
The fourth-tier side lodged their initial complaint a day after a 3-1 defeat to the Bundesliga team on 9 August, stating that Mark van Bommel had sent on six substitutes instead of the allocated five.
Following verbal negotiations, the DFB sports tribunal have sustained Preußen Münster’s objection to the outcome of their DFB-Pokal game against VfL Wolfsburg. The result has been overturned and a 2-0 win awarded to Münster.— The DFB-Pokal (@DFBPokal_EN) August 16, 2021
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Van Bommel brought on Admir Mehmedi for Maximilian Phillip in extra-time, with the match officials and Wolfsburg seemingly unaware he had already made five changes.
Announcing the sports court's decision on Monday, deputy chairman Stephan Oberholz commented: "The clubs are responsible for substitutions. One of their basic obligations is to find out about substitution options and to act accordingly.
"VfL Wolfsburg has a duty against this violated and thus frivolously and avoidably committed the central error in the inadmissible sixth substitution process.
"The club cannot invoke exonerating negligence on the part of the referee team. It can remain unanswered whether the fourth official advised those responsible at the club incorrectly or provided inaccurate information during the exchange process.
"Even if one assumes such wrong information, the main initial error is to be blamed on the club, so that any joint responsibility of the referee resigns completely."
Wolfsburg's sporting managing director Jorg Schmadtke joked after the error that those involved would be enrolled on a "basic reading course" but the 2015 DFB-Pokal winners are expected to submit a further appeal after Monday's verdict.
Schmadtke's main query centres around the match officials, who Wolfsburg claim were asked several times for clarification on the substitution quota.
In contrast, Munster's sporting director Peter Niemeyer, who took part in the DFB's hearing, said after the announcement: "We are of course very happy that the sports court ruled in our favour. Far be it from us to speak of winners or losers here.
"In an exceptional situation, a game-influencing mistake was made, which has now been subsequently corrected.
"We are of course happy for our team, which surpassed itself in the first round of the cup, for our fans and the whole environment, which can look forward to another highlight in the Prussian Stadium."
Munster is set to go into the second-round draw on 26 August, with the subsequent tie set to take place on 26-27 October.