The Croatian scored both goals as Jupp Heynckes' side continued their preparations for the second half of the season with a win which was marred by an injury to Mario Gomez.
The Germany international left the field early in the game, although his substitution is understood to have been merely a precaution.
While Bayern chose the heat of the Middle East for their training break, Bundesliga rivals Werder Bremen will probably be regretting their choice of Turkey as heavy rain and strong winds prevented them from concluding a friendly match.
It was the second day in a row Thomas Schaaf's side have suffered weather-related disruption.
Defending champions Borussia Dortmund are in Spain and they defeated Standard Liege 3-0 yesterday with Mohamed Zidan, Neven Subotic and Robert Lewandowski scoring the goals.
Elsewhere, Borussia Monchengladbach defeated league rivals Nurnberg 3-2 thanks to a double from their new signing Alexander Ring, who was making his debut days after joining the club on an 18-month loan deal.
Schalke eased to a 4-0 win over a military XI in Qatar with Chinedu Obasi making his debut following a move from Hoffenheim, and Freiburg edged out KV Mechelen by a single goal in their first game under the guidance of new coach Christian Streich.