Norway goalkeeper Orlan Nyland produced a sensational display and saved a first-half penalty from Bruno Guimaraes before Haaland struck twice in the last 11 minutes to stun Brazil at MetLife Stadium.
Neymar pulled a goal back deep into stoppage time with Brazil’s second spot-kick of the match.
Haaland’s brace took him level with Lionel Messi on seven goals for the tournament.
For Brazil, who hired Carlo Ancelotti in a bid to end a 24-year World Cup drought, it is the sixth straight tournament where they have been knocked out by European opposition.
The last time Brazil failed to reach at least the quarter-finals came 36 years ago, when they lost 1-0 to arch-rivals Argentina in last 16.
Gabriel Martinelli was rewarded for scoring the stoppage-time winner against Japan in the previous round, as the Arsenal winger replaced the injured Lucas Paqueta in the lone change to Brazil’s line-up.
Norway were boosted by the return of Julian Ryerson, the Borussia Dortmund defender fit again after missing the past two games with a thigh injury.
Patrick Berg thought he had given Norway the lead inside three minutes, but his effort was ruled out for offside in the build-up.
After a rocky start, Brazil won a penalty when Kristoffer Ajer clattered into Matheus Cunha in the box.
The Brazilians were left furious as referee Ismail Elfath initially waved away their appeals, but VAR intervened and the decision was overturned.
Guimaraes stepped up, but Nyland guessed correctly, diving low to his left to push away the Newcastle midfielder’s tame penalty.
Nyland again came to Norway’s rescue, getting a crucial touch to Martinelli’s low drive as it flashed across goal, denying Guimaraes a simple tap-in.
When Martin Odegaard lost possession on the edge of his own box, Nyland once more saved Norway as he stuck out a leg to thwart Vinicius Junior.
Haaland had struggled to make a significant impact, but his strength created a glorious opening for Norway before half-time.
The striker caused problems for Gabriel Magalhaes and Marquinhos in the Brazil defence before the ball broke kindly for Odegaard, whose effort was well saved by Alisson Becker.
Norway coach Stale Solbakken brought on Oscar Bobb and Andreas Schjelderup at the break for Antonio Nusa and Alexander Sorloth, but it was the introduction of Endrick that almost changed the game immediately.
Vinicius slipped Endrick through on goal with a delightful outside-of-the-foot pass, only for the teenager to dink wide as Nyland came out to close him down.
Nyland continued to frustrate Brazil, producing a good save to claw away Rayan’s fierce strike before making another outstanding stop to deny Guimaraes, although the offside flag went up.
The arrival of Neymar in the 67th minute drew huge roars from the largely pro-Brazil crowd.
It was Norway who eventually broke the deadlock though, and it came through an inevitable source.
Schjelderup whipped in a cross from the left and soared above Gabriel to power a header into the corner.
As Brazil desperately chased an equaliser, an incredible fingertip save from a backpedalling Nyland prevented Ajer from looping the ball into his own net.
Haaland gave Norway breathing space as he hammered low into the corner from the edge of the box in the 90th minute.
It proved vital when Neymar converted a penalty in the 10th minute of stoppage time, preceded by an unseemly spat with ‘keeper Nyland, following an elbow on Casemiro. (AFP)
