Bas Dost gave the Wolves the lead, but Sidney Sam levelled for Leverkusen on the stroke of half-time.
However, the hosts were not to be denied and Luiz Gustavo and Ricardo Rodriguez struck to take Wolfsburg to within two points of fourth-placed Schalke.
They are also now only four points adrift of Leverkusen, who cling on to second place after Borussia Dortmund's defeat to Hamburg earlier on Saturday.
Leverkusen came into the game having lost in the DFB-Pokal to Kaiserslautern, 2-1 to Schalke in the Bundesliga and 4-0 to Paris St Germain in the Champions League in the past 10 days.
Coach Sami Hyypia admitted his job was hanging in the balance and he asked his players to give him a hand, but rather than see a positive reaction, he saw them fall behind after just 13 minutes.
Ivan Perisic's low cross from the left was met by Dost in front of Bernd Leno's goal, and the Dutchman made no mistake.
Leverkusen responded well to that setback though, with Lars Bender seeing his shot tipped over the crossbar by Diego Benaglio before Sam scored on the stroke of half-time.
Stefan Kiessling put Jens Hegeler through and he pulled the ball back towards the penalty spot, where Sam was waiting to send his shot in the opposite direction to Benaglio to bring Leverkusen level.
Wolfsburg emerged for the second half like they had started the first, and they regained their lead in the 58th minute.
Ivica Olic sent in a cross from the right which was turned in by Luiz Gustavo, who was one of two Wolfsburg players left unmarked at the far post alongside Perisic.
Kevin De Bruyne was denied his first goal in a Wolfsburg shirt when Leno made a fine save to keep his free-kick out before Daniel Caligiuri was brought down by Roberto Hilbert and a penalty was awarded.
Leno guessed right to deny Rodriguez, but the Wolfsburg defender followed up to score on the rebound.
Leverkusen tried to respond with Stefan Reinartz testing Benaglio and Kiessling seeing his shot saved amid a scramble in the Wolfsburg six-yard box, but they ended up beaten again.