Augsburg secured their third win of the season with the only goal right after the re-start, a powerful free-kick from former Gladbach player Jan-Ingwer Callsen-Bracker deflecting in off Gladbach's Raul Bobadilla.
Borussia have now failed to win for the second straight match without injured striker Marco Reus.
"We did not underestimate Augsburg. We just made far too many mistakes against a team that played very clever," said Gladbach defender Martin Stranzl.
The hosts took a 20th minute lead through defender Sokratis Papastathopoulos and striker Claudio Pizarro netted on the stroke of halftime, catching the Wolfsburg defence napping for his 12th goal of the season.
Forward Markus Rosenberg added a third 10 minutes after the restart and Marko Arnautovic completed the demolition after a nice pass from Pizarro. Marcel Schaefer cut the deficit with four minutes left.
Felix Magath's Wolfsburg have now won only one of their last seven matches to drop to 14th, three points off the relegation zone.
Bremen coach Thomas Schaaf said: "We came in well. The team played very well apart from early in the second half. There were lots of chances from both sides and the result could have been a completely different one."
For Hanover, who are eighth, it was the fourth draw in the last five games and their sixth match without a win.
Ibisevic added another early in the second half to lift Hoffenheim to ninth place.
Hamburg SV continued their unbeaten run stretching back to mid-October with a goalless draw at Mainz 05.