After being a non-factor for much of the afternoon on Sunday (Monday AEST) and having limited touches, Haaland turned it on when it mattered most, getting the right side of his head on the ball after a perfect setup by Andreas Schjelderup, who entered at halftime.
Schjelderup jumped on Haaland's back to celebrate the 6-foot-5 striker scoring his sixth goal at the World Cup and did so again after assisting on his seventh.
Haaland extended his streak of scoring to 14 consecutive competitive matches internationally and he joined Argentina's Lionel Messi and Kylian Mbappé of France for the most goals in the tournament.
At the other end, goalkeeper Orjan Nyland was stellar. He made a crucial stop early, diving to his left to deny Bruno Guimaraes' penalty kick in the 14th minute, then got his left hand on a shot by Endrick late when Norway were hanging on to a one-goal lead.
The only goal Nyland allowed was to Neymar on a penalty kick late in stoppage time, which changed just the final score.
Nyland, who at 35 is his team's oldest player, was a huge factor in a historic victory that ranks among the most significant in the country's history, at least on the men's side.
Norway's women's team won the World Cup in 1995, but the men have only qualified four times and not since 1998. They had not gone further than the round of 16.
Norway next face the winner of the Mexico-England round-of-16 game, with the quarter-final matchup to take place on Saturday in Miami Gardens, Florida.
Guimaraes became the first Brazil player not to score on a World Cup penalty kick since Zico in 1986. The decision to have him take it instead of star Vinícius Junior brought immediate second-guessing and may be questioned and criticised for quite some time.
There were plenty of other missed opportunities, including Casemiro missing Neymar on a crossing attempt on what could have been the tying goal.
Brazil go home having massively underachieved expectations set pretty much at win or bust for the five-time World Cup champions. The global powerhouse had their streak of quarter-final appearances at the tournament end at eight, losing before that stage for the first time since 1990.
It was also Brazil's seventh consecutive loss to European opponents at the World Cup, dating to beating Germany in the 2002 final.
