Louis van Gaal's men appeared to be staring defeat in the face during their last-16 clash on Sunday, as Giovani Dos Santos gave the North American nation a deserved lead just after the break.
But the Dutch fought back and dominated the majority of the second half, drawing level in the 88th minute thanks to Wesley Sneijder.
Huntelaar eventually netted the all-important second goal, converting a penalty with admirable composure in the fourth minute of stoppage time, but the Schalke man was in two minds before taking the kick.
The 30-year-old had missed four of his previous five spot-kicks and he acknowledged that he almost changed his mind about taking the penalty.
"I didn't have the balls to shoot it down the middle," he told NIS.
"Arjen [Robben] had the ball and asked 'would you like to take it?' When I was there I thought about changing [my mind], as I had missed the last time.
"[But] what an adrenaline rush. This is the best drug out there."
Robin van Persie endured a disappointing day individually as he was hauled off for Huntelaar in the second half and he recognised that the excessive heat and humidity had made conditions tough.
"It was very tough," the Manchester United forward added.
"When you are losing you want to attack, but you also need to make sure the space at the back is not too great. Then the heat - it made it extra hard.
"We now have to deal with the next round. We are good, I believe in us and that we must continue to do so [believe in themselves]."
Netherlands will now face Costa Rica in the quarter finals after the latter's shootout win over Greece.