Manchester City striker Haaland now has five goals in three games at the tournament, taking his international total to 60 in 53 appearances, and Norway will face Brazil next.
It was Antonio Nusa who struck first, curling a stunning right-footed finish into the top corner on 39 minutes after Martin Ødegaard's layoff, against the run of play. Ivory Coast had dominated the early stages, with Yan Diomandé and Nicolas Pépé giving Norway's backline a difficult evening.
The second half belonged to Amad Diallo. The Manchester United winger came off the bench and within minutes had cleared Torbjørn Heggem's goal-bound effort off the line. Seven minutes later he was at the other end, combining with Pépé and driving into the box to crash in an equaliser on 74 minutes.
As extra time loomed, Oscar Bobb found Sander Berge wide on the right, and his cross was turned in by Haaland from close range. Goalkeeper Ørjan Nyland then denied Diallo a dramatic injury-time free-kick to complete the win.
Ivory Coast head coach Emerse Fae was proud of his side despite the defeat.
"That's football. When you get chances, you have to score. We did the hard part by equalising. Unfortunately, we conceded that goal at the end. It's a shame.
"The players gave it their all and played until the very end. We were up against a spirited team that defended well and managed to secure qualification.
"At this level, it comes down to the little details. You have to stay focused from start to finish, no matter the opponent. It was everyone's first World Cup. I think the players have learned a lot. Now, we'll work on coming back stronger for the next challenges."
Midfielder Franck Kessié reflected on the margins that cost them.
"This elimination leaves a very bitter taste. We had a real chance. Once again, some little details stop our momentum in the competition. It was a 50-50 game. They managed to capitalise on their chances. Unfortunately, there were moments we lacked composure. It was a game defined by transitions. You have to know when to slow the pace, like with Amad's goal, which was a well-constructed move — but we shouldn't have only a vertical play."
Norway coach Ståle Solbakken was emotional about what the result means for his country.
"If I survive this, I will survive everything. The fact that we are able to come back is perhaps what I am most proud of. It has been 28 years since we last participated, we have taken on the USA and won three out of four games. Our supporters have taken the USA by storm.
"It's a kind of suffering you probably can't get anywhere else — a feeling that you simply can't get from any other match. We played against a fantastic team who have some absolute monsters, physically, who got the better of us in the duels at times. The match swung back and forth, it looked like it could go either way. I think we had one or two more chances than they had so all in all, it was a deserved win. But I feel for their coach — the margins were slim."
Haaland dedicated the win to the travelling Norwegian support.
"It's nice to see that it means so much to all of Norway. I think this will change Norway forever. I feel this is something that binds us a little extra together, it's simply touching to see."