Donyell Malen, Maximilian Beier and Julian Brandt were on target between the 25th and 30th minutes in Sunday's clash, but Wolfsburg fought back through Denis Vavro in the 58th before Dortmund's Pascal Gross was red-carded four minutes later.
But Dortmund prevailed to win away for the first time in their seventh league attempt of the season, having previously lost four and drawn two.
They were rewarded with a rise to sixth place, tied on points with Mainz ahead of them and two points off the top four, as they ended the year on a positive note.
Dortmund, playing the last top-flight game of the year in Germany, will also start the second part of the season on January 10 when they host champions Bayer Leverkusen.
Bayern Munich are hibernating on top four points ahead of Leverkusen, with Dortmund 11 points behind the leaders.
"It feels good. We played a great first half. We were very efficient. We wanted to continue that way but it didn't work out. But we won," Beier said.
"We want to do better next year. It can't be our ambition to be sixth."
In Sunday's other game, bottom club Bochum got their first season victory at last on matchday 15 when they beat fellow strugglers Heidenheim 2-0, with goals from Moritz Broschinski in the sixth minute and Matus Bero in the 38th.
Bochum doubled their season haul to six points after previously managing only three draws.
They remain last, two points behind Holstein Kiel, and four off Heidenheim who are in the relegation play-off spot after a ninth defeat from 10 games without victory.
"We have taken the biggest step today after so many failures. I'm absolutely delighted. It's a little pre-Christmas present for all of us at VfL," Broschinski said.
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