Tobias Werner gave Augsburg the lead in the fifth minute of a game they dominated from start to finish, but two chances were all Schalke and Huntelaar needed to turn things around and take the Royal Blues up to third.
Augsburg will wonder how they had not managed to continue their own push for a place in Europe after creating enough chances to win several matches, only to come away empty-handed.
Augsburg moved into the top six last weekend and the scent of European football was getting stronger in the Bavarian city.
It was particularly pungent in the fifth minute when Werner put them in front, slotting the ball past Ralf Fahrmann after Sead Kolasinac made a mistake with Alexander Manninger's long ball.
Augsburg continued to take the game to their opponents and Raul Bobadilla almost set up a second for Halil Altintop, but his cross was just behind the Turkish striker.
Both Altintop and Bobadilla missed the target with shots from distance and Werner also went close before Huntelaar hit the stanchion behind the goal with Schalke's first shot of the game.
It was a warning which was followed by a goal from the Dutchman, who was on hand to tuck the ball in after Manninger only parried Kevin-Prince Boateng's effort.
Augsburg were unfortunate to concede, having dominated the game up to then, but the goal took the wind from their sails and Schalke started to settle.
Four minutes into the second half, Schalke's best move of the match saw them take the lead.
Kolasinac was put through on the left by Julian Draxler and his low cross gave Huntelaar an open goal, which he was not going to miss from five yards out.
Schalke's efficiency was exquisite, but the Augsburg fans kept their spirits high and their team responded.
It was one-way traffic in the second half, like in the first, but all that was lacking was a finish.
Ji Dong-Won came on and sustained Augsburg's search for an equaliser, with Fahrmann increasingly in the firing line.
Altintop volleyed over and Andre Hahn sent a shot over the crossbar from just outside the penalty area as the Bavarians tried in every way they could to level.
They were ultimately unable to find a goal, though, as Schalke got away with a fortunate win which took them up to third in the table ahead of Bayer Leverkusen's trip to Bayern Munich on Saturday evening.