Emil Forsberg fired the unbeaten side to its fourth win in seven games, putting it level on points with another surprise team, Cologne, and just two points behind leader Bayern Munich.
The Swedish midfielder missed the chance to score from the penalty spot in the first half, sending his effort to the left of Koen Casteels's goal after the Wolfsburg goalkeeper had brought down Timo Werner.
It was the fifth missed penalty of the weekend, a record for a single round of games in the Bundesliga.
Antonio-Mirko Colak had earlier missed a penalty for Darmstadt in his side's 2-1 loss at local rival Mainz; Borussia Moenchengladbach's Andre Hahn and Lars Stindl both squandered penalty chances in their side's 0-0 draw with Hamburger SV on Saturday; and Borussia Dortmund striker Pierre-Emerick Aubameyang had his spot kick saved by Hertha Berlin's Rune Jarstein in the 1-1 draw on Friday.
Ten penalties were awarded across the nine games, the most in a Bundesliga round since the 1986-87 season.
Forsberg made up for his penalty miss with a brilliant strike from outside the penalty area to the top right corner with 20 minutes remaining. It was the Swede's third league goal of the season, catapulting Leipzig above Hertha in fourth place and Dortmund in fifth. Four points separate the top six.
• WATCH: Lionel Messi scores minutes after return from injury
Wolfsburg coach Dieter Hecking's position is in question after his side slipped to 14th, following its sixth consecutive game without a win.
"We're going to have to talk within the club, what we're going to do in future, where we see the possibilities of playing better football again," Wolfsburg general manager Klaus Allofs said. "That can be with the coach, it can also be without the coach."
Mainz 2, Darmstadt 1
In a game with three penalties, Mainz claimed its third win to move seventh.
Colak should have made it 1-1 before the break when the first penalty was awarded but Mainz 'keeper Jonas Loessl saved his spot kick.
This article originally appeared on 
