The play-off tie turned just 14 minutes into the second leg when Wolfsburg defender Joakim Maehle was sent off after picking up two quick yellow cards.
Although Wolfsburg had made the perfect start through Dzenan Pejcinovic after only three minutes, the red card completely shifted the momentum.
Paderborn sporting director Sebastian Lange admitted the dismissal helped his side, but praised the performance and intensity shown by the players throughout the match.
"The way the match developed played a bit into our hands with the second yellow card," Lange said.
"But I have to say the lads really surpassed themselves today. How sharp we were, how quickly we moved the ball - everyone did really well.
"It was a great performance. That's why it was deserved."
Paderborn quickly took control after Wolfsburg were reduced to 10 men and finally levelled the match through Filip Bilbija, who headed home from close range after excellent work from Calvin Brackelmann.
The home side dominated for long periods, finishing normal time with an incredible 31 shots compared to Wolfsburg's two, but extra-time was needed to decide the contest.
The winning moment finally arrived before the 100-minute mark when veteran forward Sven Michel delivered a cross to the far post for Laurin Curda, who volleyed home to spark wild celebrations inside the Home Deluxe Arena.
Wolfsburg coach Dieter Hecking was left frustrated by the early sending-off and questioned the referee's decision after the match.
"When it comes to the red card, you have to look at the entire sequence of events," Hecking said.
"We would have liked the referee to show a bit more feel for the situation. But it's pointless now - the match is decided. We have to congratulate Paderborn."
The defeat confirmed Wolfsburg's first relegation from the Bundesliga, while Paderborn completed a remarkable return to the top flight for the third time in the club's history under first-year coach Ralf Kettemann.
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