Marco Reus completed the comeback after 77 minutes with his 13th goal of the season - and fifth in four league games - after Robert Lewandowski had cancelled out Ivica Olic's opener.
Dortmund's victory lifted them three points clear of Schalke in the race for second, with the latter having been held to a 1-1 draw at Werder Bremen earlier on Saturday.
The result also provided a boost for Jurgen Klopp's side, who are 20 points behind Bundesliga champions Bayern, after their 3-0 defeat to Real Madrid in midweek, which has left them facing likely elimination from the UEFA Champions League ahead of Tuesday's second leg.
Reus had scored each of Dortmund's last four goals in the Bundesliga before the fixture and almost grabbed another after eight minutes, but his shot from the left was saved.
Wolfsburg's Olic then missed a chance to open the scoring from close range when he got on the end of Robin Knoche's cross from the right, while Reus tested Max Grun again following a nicely weighted throughball from Lewandowski.
Langerak had to react quickly to punch over from a Max Arnold cross after 24 minutes, with the effort taking a wicked deflection which nearly looped over the goalkeeper's head.
Olic incredibly struck the crossbar twice just before the break as he slid in to reach a cross from De Bruyne. The forward's initial attempt came back off the woodwork before the ball rebounded off his left foot to hit the bar again.
The changes paid dividends as the hosts found an equaliser six minutes after the restart when Lewandowski bravely got on the end of Reus' corner from the left to score with a somewhat unorthodox header.
