The Manchester City predator had a quiet afternoon at the home of the Dallas Cowboys before prodding home in the 86th minute for a thrilling 2-1 victory over the Ivory Coast.
It was Norway's first win in a World Cup knockout match and Haaland told broadcasters: "This is unbelievable.
"I can't swear, but it is unbelievable. This is history."
It was Haaland's fifth goal in three games in North America, having been rested for the 4-1 loss to France in the group phase
His late winner means he has scored in each of his last 13 competitive internationals for Norway, scoring 25 goals in that run.
Norway will be underdogs against Brazil but captain Martin Odegaard said with Haaland up front they always had a chance.
"It's amazing to have him in the team, we're lucky to have him and it's just about giving him as many opportunities as possible," he said.
Stale Solbakken, Norway's coach, hailed the 25-year-old Haaland as "the greatest goalscorer in the world".
"There's no doubt about that. Today he wasn't that much involved. I think he had one big chance in the first half, and now he's scored the winning goal again.
"It brings a calmness to the team when you have a player like him, who is in my way very underrated in terms of keeping the ball.
"Because you see he didn't lose one ball today.
"To score five goals in the World Cup in three games, for a little country like Norway... I wouldn't swap him for anyone.
"Because he's the greatest goal scorer in the world of football today."