Virgil van Dijk’s first-half header had put Jurgen Klopp’s side on course for a fourth win in five pre-season games.
However, Christian Pulisic levelled from a penalty and added a second before Jacob Bruun Larsen rounded off the scoring for the Germans.
The Reds were again without a number of key players after the World Cup.
Mohamed Salah, Sadio Mane and Marko Grujic all watched from the side at the Bank of America stadium after only returning to training on Friday.
Liverpool’s world record goalkeeping signing Alisson was also unavailable for selection, and in his absence Karius contributed to Dortmund’s final goal, diverting a Pulisic effort into the path of Bruun Larsen to complete the victory.