Douglas Costa's goal helped Bayern Munich edge Wolfsburg 1-0, while Borussia Monchengladbach cruised 2-0 past Greuther Fuerth in German Cup.
Bayern Munich ended the 2015-2016 season with the domestic double after beating Borussia Dortmund 4-3 on penalties at outsold Berlin's Olympic stadium.
Pep Guardiola will leave for Manchester City next season and Dortmund defender Mats Hummels will join Bayern Munich.
Bayern Munich and Borussia Dortmund advanced from the opening round of the German Cup on Sunday, while Hamburger SV was knocked out by Carl Zeiss Jena.
It looked liked Bayern could protect their neat 1-0 lead to the end but Wolfsburg's Nicklas Bendtner restored parity in the dying minutes of the game
Wolfsburg shocked Bayern with the late 1-1 equaliser to wrap up the German Supercup 5-4 on penalties at Volkswagen Arena.