After an even opening, Andre Schürrle broke the deadlock towards the end of the half. He carried on that form into the second, scoring twice to secure his hat-trick.
Julian Draxler added a classy fourth, in what was a performance that the Wolves' fans would have been craving for a long time.
Schürrle edges Wolfsburg ahead
It was a quiet start ot proceedings on the pitch in Hannover, despite a pyrotechnics display from the fans in the stands. Wolfsburg looked more confident in possession and played in a few dangerous crosses, though they came to little.
The hosts did, however, have an early sight at goal when Kenan Karaman was played in by Hiroshi Kiyotake, but couldn't quite find a way past Diego Benaglio.
Wolfsburg soon got going, but found Ron-Robert Zieler in his usual excellent form. The Hannover custodian denied Julian Draxler's long-range effort, before pulling off an even better reaction stop to deny Luiz Gustavo's header from just a few yards out. Thomas Schaaf's side had lost all their early momentum, and were made to pay.
A swift break by the Wolves found Draxler driving at the heart of an already outnumbered home defence. The visitors had two men over on the far side, one being Andre Schürrle, who took full advantage. The forward finally found the net after steadying himself, managing to put his shot past the outstretched hand of Zieler and in off the post.
Visitors turn on the style
The second half began as the first ended, with Wolfsburg on top. Draxler was involved again, as he slid in Max Kruse after a driving run. The striker was kept out well by Zieler, although the rebound fell kindly to Schürrle; however, a stunning block from Christian Schulz and another stop from Zieler kept him at bay.
The respite lasted no more than a minute, as the resulting corner provided the former Chelsea man with his second goal. Luiz Gustavo was able to bring down the set-piece, leaving Schürrle free to run onto the ball and slam a sweetly struck half volley into the bottom corner.
His second was good, but the attacker's third was even better. After a cross was only half cleared by the Hannover defence, Schürrle chested it down and sent a stunning volley past the helpless Zieler; the hosts could barely believe their eyes, Wolfsburg were in total control.
It would get worse still for Schaaf's charges, as Julian Draxler added a fourth. A classy counter, similar to the first goal, saw a raking pass from Kruse find the run of Draxler, who made no mistake when one-on-one with Zieler, finishing with aplomb.
Wolfsburg closed the game out for the three points and closed the gap on the top six, although they are all yet to play. Hannover lost now ground on their relegation rivals as, similarly to the Wolves, the teams immediately above them haven't taken to the field; they could, however, find themselves seven points from safety by Wednesday evening.