The sides drew 1-1 on Tuesday and agreed to a rematch as Aberdeen's original second opponents, the Tunisian national team, had pulled out.
Former German international Thomas Hassler gave Munich a half-time lead. His corner from the left went straight past goalkeeper Ryan Esson.
Robbie Winters and Andy Dow wasted chances before substitute Darren Mackie levelled just after the break.
The 19-year-old collected a Rachid Belabed through ball and finished cooly.
Hassler restored 1860's advantage with a penalty on the hour mark after Kevin Rutkiewicz had brought down Markus Beierle.
But substitute Darren Young made it two apiece with a powerful long-range effort in stoppage time.