Muller and Klose bag Bayern Super Cup win
Muller, who on Friday extended his contract with the club until 2015, opened the scoring in the 75th minute as coach Louis van Gaal chose to field five of the seven Bayern players in the Germany World Cup squad, even though they only started training this week.
Bayern substitute Andreas Ottl sent a long pass forward which Schalke goalkeeper Manuel Neuer failed to clear and Klose left the ball to Muller - joint top scorer in South Africa with five goals - who steered it into the empty net from the edge of the area.
Six minutes later, Ivica Olic twisted past his marker to deliver a low ball which Klose converted from close range.
The German Supercup, between the winners of the previous season's Bundesliga and German Cup, was officially reinstated by the German federation this year after a 14-year absence.
As Bayern won the double last season, they met Bundesliga runners-up Schalke 04.