The Colombia midfielder, 27, nodded home from the edge of the six-yard area following an early corner.
Bayern dominated the game in Gelsenkirchen.
David Alaba hit the bar before Robert Lewandowski made it 2-0 from the penalty spot after Rodriguez was fouled.Bayern, chasing a seventh successive Bundesliga title, are two points clear at the top of the table after four games.
Niko Kovac's side entertain mid-table Augsburg (19:30 BST) on Tuesday before travelling to meet second-placed Hertha Berlin on Friday (19:30 BST).
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Bundesliga