Tobias Werner put the visitors in front with three minutes remaining in the first half, but Ivica Olic equalised for Wolfsburg late in the match.
Augsburg's compact defensive unit disrupted any Wolfsburg flow to the game, which infuriated coach Dieter Hecking on the sidelines.
The closest attempt from the Wolves was through young midfielder Maxi Arnold on 12 minutes. The Wolfsburg academy graduate broke away from a few challenges and struck left-footed from 25 yards, but his shot trickled wide.
Instead the impressive Augsburg, who are just outside of the top six and European football, took the lead against the run of play on 42 minutes.
Some slack Wolfsburg passing opened up a fast-break opportunity for Halil Altintop and he introduced Werner, who left two defenders in his wake before curling a shot into the corner.
Markus Weinzierl's side leapfrogged the Wolves momentarily in the standings as the game ran out of momentum late on.
However, Wolfsburg struck with eight minutes remaining to level the scores when Ricardo Rodriguez picked out the head of veteran Croatian striker Olic, who glanced home.
The result means Augsburg remain two points shy of their opponents in the table, while Wolfsburg have not tasted victory in the Bundesliga since beating Bayer Leverkusen last month.