The Dutchman displayed clinical form in front of goal to guide Jens Keller's men to a victory that sees them leapfrog Bayer Leverkusen into third place ahead of their visit to Bayern Munich on Saturday.
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However, the visitors had looked set for a defeat against sixth-placed Augsburg, who themselves have hope of a place in the top four, when Tobias Werner put Markus Weinzierl's side in front after just five minutes.
Midfielder Werner capitalised on an ill-advised header back to goal from Schalke defender Tim Hoogland to slot a cool finish past Ralf Fahrmann and into the bottom corner.
But Schalke found a way back into the game 12 minutes before half-time as Huntelaar netted his first.
The striker tapped in a rebound from close range after Kevin-Prince Boateng had been skillfully played in by Julian Draxler, only to see his effort saved by Alexander Manninger.
And Huntelaar completed the turnaround four minutes after the interval, slotting home from Sead Kolasinac's pull-back to finish off a sweeping move from the visitors.
Draxler then had a goal disallowed for offside, but that proved immaterial as Schalke hung on despite a late onslaught from the hosts.