James, on loan from Real Madrid, scored the second goal and cleverly set up the third, having also played a part in winning the penalty which got Bayern off the mark.
Robert Lewandowski fired Bayern ahead from the spot in the 25th minute after James got to the byline and produced a cross which was handled by Naldo.
Four minutes later, James got free in the Schalke box and tucked his shot past Ralf Faehrmann for Bayern's second.
Not content with that, he cut inside two defenders and dinked the ball over the Schalke defence for Arturo Vidal to add the third in the 75th minute.
Bayern's win put them on 12 points from five games and took them top, at least until Wednesday.
Augsburg continued their impressive start when a fourth-minute goal from Michael Gregoritsch gave them a 1-0 win over last season's runners-up RB Leipzig.
VfL Wolfsburg drew 1-1 at home to Werder Bremen and Borussia Moenchengladbach beat VfB Stuttgart 2-0 in the other games.
(Writing by Brian Homewood; Editing by Toby Davis)
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