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There was concern for the hosts early on as Julian Draxler went down with an upper leg injury inside the opening minute, and was unable to continue.
After an otherwise quiet opening half-hour, Halil Altintop came close to putting the visitors ahead, but a block on the line ensured that the sides remained level.
The deadlock was broken shortly before the break though when Huntelaar collected a through-ball from Atsuto Uchida before slotting it into the bottom left corner.
The striker could have added a second shortly after the hour mark when he was left unmarked in the Augsburg box, but the visitors had a man back to make sure that the keeper remained untroubled.
They could have put the win beyond doubt late on when Obasi tried a long-range effort, but Hitz watched it all the way to make sure it did not find the target.
The result moves Schalke up to seventh in the table, while Augsburg sit 12th.