The German champions have not played since beating Mainz 2-1 in the Bundesliga on December 19, but never looked in danger of losing against the Qatari top-flight's representative side.
Mitchell Weiser opened the scoring inside the opening three minutes - Thomas Muller finding himself in acres of space in the Stars' box before teeing up the 20-year-old for a simple finish.
Weiser, who is yet to find the net for the senior team, doubled the visitors' advantage 12 minutes later when he cut in from the right and rifled an effort across goalkeeper Claude Amin.
However, the Stars - managed by Lekhwiya coach Michael Laudrup - reduced the deficit against the run of play after 27 minutes.
Al-Arabi's Pablo Hernandez, who formerly played under Laudrup at Swansea City, beat the offside trap and darted down the right wing, before playing a low cross to Hamdi Harbaoui, who slotted home.
Franck Ribery found the net following a Sebastian Rode cutback shortly before half-time to re-establish the two-goal advantage, but scoring did not come as easily for Bayern after the interval.
One of the biggest second-half positives for Pep Guardiola was the introduction of injury-plagued Holger Badstuber, who has been out since September with a thigh injury.
Bayern finally added to their haul in second-half stoppage time, when Claudio Pizarro gratefully tucked the ball into the bottom corner after being left totally unmarked at a corner.
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