Antonio Nusa grabbed his ninth international goal to give Norway a half-time lead, but Manchester United's Amad Diallo levelled things up with a moment of magic before Haaland scored in his 13th straight competitive international to send Norway through.
It was Ivory Coast who looked like they would take the lead, and they should have done so when Yan Diomande's cross found Nicolas Pepe inside the area, but he decided to cushion a volley back across goal when it looked easier to strike.
Norway hit the front six minutes before the break in spectacular fashion. Martin Odegaard found Nusa inside the box who cut inside and curled a brilliant effort into the top corner.
Haaland threatened to double Norway's lead when the ball fell nicely for him inside the area but his goal-bound effort was brilliantly blocked by Ibrahim Sangare.
Ivory Coast continued to look threatening in their search of an equaliser. Pepe seemed the danger man and he almost levelled but his low drilled strike was saved by Orjan Nyland.
Amad made a pair of game changing contributions – after he stopped Torbjorn Heggem on the line down one end, he went down the other and weaved in and out of the scrambling Norway defenders before dispatching perfectly into the bottom corner to level matters.
But Norway snatched the winner four minutes from time, Oscar Bobb's ball found Odegaard who squared for Haaland who then had the simple job of tapping home for his 60th international goal.
It was the Manchester City star's fifth goal of the tournament, one behind leader Lionel Messi of Argentina.
Norway will meet Brazil on Sunday in New Jersey with a place in the quarter-finals at stake.
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