After Nico Elvedi put the hosts ahead early on, a quickfire Erling Haaland brace turned things around, only for Elvedi to notch his second to make it 2-2 after 32 minutes.
Ramy Bensebaini and Marcus Thuram then added second-half efforts for Monchengladbach as they secured a fourth win in five games.
In Serie A, a stoppage-time Simone Zaza goal secured relegation battlers Torino a 2-2 draw at Benevento in their first match under Davide Nicola.
Simone Zaza, left, celebrates his equaliser (Alessandro Garofalo/AP)
The home side were 2-0 up through a Nicolas Viola penalty and a strike from Gianluca Lapadula before Zaza reduced the deficit with a header, then drew things level late on.