Schalke moved up to third place for the first time under coach Jens Keller, who took over in December 2012, with 47 points from 25 matches, three ahead of Bayer Leverkusen before their Saturday trip to runaway leaders Bayern Munich.
Werner put the Bavarian hosts ahead after five minutes but Huntelaar, who has nine league goals in 10 matches this season, equalised in the 33rd from close range after Augsburg keeper Alex Manninger blocked a long-range Kevin-Prince Boateng shot.
Huntelaar got what would prove to be the winner four minutes after the break by finishing off a move involving Boateng, Orcun Ayhan, Julian Draxler and Sead Kolasinac, whose cross from the left found the Dutchman unmarked near the penalty spot.
Sixth-placed Augsburg, who have 38 points from 25 matches and are hoping to qualify for Europe, kept the pressure on until the final whistle but squandered a handful of chances.
"It was hard after we fell behind 1-0 in just five minutes," said Keller, whose team have seven wins and two draws in their last 10 matches. "We didn't get into the match at all."
Bayern have 68 points, 20 clear of second-placed Borussia Dortmund who host Borussia Moenchengladbach on Saturday (1430).
- Sports & Recreation
- Jens Keller
- Bayer Leverkusen
- Alex Manninger
- Kevin-Prince Boateng