Tunisian central defender Karim Haggui was man of the match for all the wrong reasons, twice scoring in his own net, with Constant Djakpa adding another own goal to stun Hanover's fans.
"We saw a crazy, curious match," said Hanover coach Andreas Bergmann. "It's unbelievable we scored six goals and lost the match. I don't think we'll forget this match any time soon."
Haggui's first put the hosts ahead after 15 minutes but was not his fault as goalkeeper Florian Fromlowitz slipped and kicked the ball onto the defender's foot and back into the net.
His second in stoppage time, a back pass from 18 metres that sealed Gladbach's win just minutes after Hanover had cut the deficit to 4-3, left the 25-year-old smiling over his bad luck.
Djakpa's back pass from 18 metres that surprised his keeper was equally spectacular and could not have come at a worse time, with Gladbach leading 2-1 and Hanover pushing for the equaliser.
Ivorian Didier Konan had netted twice for Hanover to keep them in with a chance but was sent off for a second booking six minutes from time.
