Manchester United’s Amad Diallo was sent on for the Ivory Coast after an hour and was immediately in the thick of it, stopping a certain second Norway goal and then grabbing a terrific equaliser on 74 minutes.
With extra time looming, predator supreme Haaland got on the end of a cross by Patrick Berg to make some Norwegian history.
They face five-time champions Brazil on Sunday in New Jersey with the quarter-finals at stake.
A match between two physical teams was tepid to begin with at the impressive, air-conditioned home of the Dallas Cowboys in the United States.
Ivory Coast had a sight of goal after 20 minutes, with defender Ghislain Konan bursting into the Norway box from the left but finding the side netting.
The Ivory Coast players and fans were irate just before the drinks break when the livewire Yan Diomande was brought down on the break just inside his own half.
Referee Jesus Valenzuela surprisingly did not even book defender David Moller Wolfe.
The 19-year-old winger Diomande, who appears set to join European champions Paris Saint-Germain from RB Leipzig, was growing into the game.
The African side, one of the youngest at the tournament, were on top and particularly threatening down Diomande’s left-hand side of the pitch.
Haaland had little to feed on but might have done better with a tame header that bounced into the hands of goalkeeper Yahia Fofana.
Then came a moment of genuine class as Nusa, fed by captain Martin Odegaard, cut inside and bent the ball wonderfully into the top corner.
Odegaard put his hands on his head in disbelief at the strike by the 21-year-old, Diomande’s Leipzig teammate.
Stale Solbakken’s Norway finished the first half on the hunt for a second and Haaland was denied by a last-gasp block by Ibrahim Sangare, who celebrated as if scoring a goal.
The Ivory Coast, into the knockout rounds for the first time, won their 10th corner to start the second half.
Nicolas Pepe was denied by the legs of Norway stopper Orjan Nyland as the Ivory Coast piled on the pressure.
Norway, runners-up to France in the group stage, were inches away from a second when Diallo blocked the ball on the goal line following a corner.
The Norway fans, sensing the next round was close, began their now-famous rowing in the stands.
Almost as soon as they stopped, Diallo danced into the box past two challenges for a spectacular leveller.
Then up popped Haaland to break Ivorian hearts, with goalkeeper Nyland pulling off a flying stop from Diallo’s well-struck free kick at the death to send Norway through.
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