Two goals from the hosts' star striker in extra time was just enough in a tough, physical battle that appeared headed to penalty kicks until the Dutchman struck
After a 1-1 draw in the first leg a week ago, where Huntelaar scored 15 minutes from time to draw things level, the Germans aimed to continue their success at home, where they haven't seen defeat since mid-October, and things got off to a cracking start thanks to their attentive attacker.
Seven minutes in, Julian Draxler was played into space in the middle of the pitch, and the midfielder marched towards goal before firing a straight shot at goalkeeper Marek Cech, who made contact to parry the effort.
Huntelaar was on hand for the rebound from the left side of the box, finishing calmly into the net as the visiting custodian could not recover.
With the crowd going wild, the Czech side were desperate to get back into the contest. Needing a goal to draw level on aggregate, Viktoria seemed to have found one nearly a half an hour in, but Marian Cisovski's header into the net from close range was ruled as offside.
After an uneventful start to the second half, Marek Bakos was shown a red card for a foul on Kyriakos Papadopoulos with 30 minutes to go, leaving the visitors with 10 men, and seemingly up against it.
Several missed chances from Schalke followed and they would ultimately prove costly as Viktoria responded via Frantisek Rajtoral two minutes from time.
The Czech player fired home from inside the box with a volley that stunned the home fans. and meant that the match was heading for two additional periods.
However, in extra time, Huntelaar managed to net after a cross from Obasi Ogbuke found the striker perfectly in the middle of the box, where he sent a powerful effort into the net to secure the win.
Just seconds before the conclusion of the match, Huntelaar added another goal from close to put the match away and break the spirit of the valiant visitors, who gave their all.
With the result Schalke advance to face Twente in the round of 16 on March 8.