Braunschweig goalkeeper Daniel Davari inadvertently gave Gladbach a first-half lead and Ter Stegen returned the compliment when he failed to control a back pass and instead knocked the ball into the net shortly after the break.
Werder Bremen eased their relegation fears and left arch-rivals Hamburg SV in deep trouble after a 1-0 win in the 100th Bundesliga meeting between the old rivals, northern Germany's two biggest clubs.
Borussia Dortmund moved into second place with a 3-0 win over Nuremberg, Robert Lewandowski getting among the scorers to take his tally for the season to 15, and overtook Bayer Leverkusen who lost 1-0 at home to Mainz 05.
Ter Stegen's misfortunate was almost a replica of the goal he conceded in Germany's 4-3 friendly defeat to the United States last year when he completely missed a back pass and the ball rolled into the net.
There was not the slightest danger when Filip Daems rolled the ball back to Ter Stegen, who was not even in front of his goal. However, the hapless goalkeeper miskicked the ball completely and it rolled into the net amid general disbelief in the 52nd minute.
The goal spared Davari's blushes after he attempted to block a corner at the near post, only for the ball to bounce into the net off his knee.
Zlatko Junuzovic scored the only goal as Bremen sank Hamburg SV, who reverted to losing ways after last week's 3-0 win over Dortmund had ended a seven-month winless run.
The defeat left Hamburg, the only ever-present team in the Bundesliga's 51-year history, in 16th place, the relegation playoff spot with 19 points, ahead of Freiburg on goal difference. Braunschweig have 16 points.
Dortmund completely dominated their match and only an outstanding performance from Nuremberg goalkeeper Raphael Schaefer prevented the hosts from doubling their tally. Mats Hummels, Lewandowski and Henrikh Mkhitaryan shared the goals for last season's runners-up.
Erik Maxime Choupo-Moting scored the only goal as Mainz handed fading Leverkusen their third successive Bundesliga defeat.
- Sports & Recreation
- Ter Stegen
- Borussia Dortmund
- Bayer Leverkusen
- Robert Lewandowski
- Hamburg SV
- Daniel Davari