It was the second win in three league games for coach Roberto Di Matteo, who took over from Jens Keller this month, but his team looked far from convincing ahead of the trip to Lisbon to face Sporting in the Champions League next week.
Schalke suffered an early blow when attacking midfielder Julian Draxler went off with a thigh injury after a few seconds.
Japan international Atsuto Uchida, who on Thursday signed a three-year contract extension, set up the 37th-minute winner with a spectacular solo run and cut-back for Huntelaar to grab his fourth league goal of the season.
Schalke, who have 14 points from 10 games, failed to carve out any more scoring opportunities with Augsburg much the livelier team in the second half.
Substitute Tim Matavz almost equalised in stoppage time when he weaved his way past two Schalke defenders but fired wide as the visitors remained in 12th position on 12 points.
Bayern entertain last season's runners-up Borussia Dortmund on Saturday.
(Reporting by Karolos Grohmann, editing by Tony Jimenez)
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