The Manchester City striker scored his 63rd and 64th goals for Norway in his 56th appearance, moving beyond Ibrahimovic's 62 goals in 122 matches for Sweden.
Haaland completed his double in the 74th minute to secure Norway's first competitive victory over Denmark.
Norway manager Stale Solbakken believes the striker's extraordinary goalscoring ability is something that cannot be taught.
"It is not possible to explain, nor is it possible to learn. He is born with it. It is instinct," Solbakken said.
Haaland made his senior Norway debut in 2019 and has now scored more than once per game on average for his country.
Norway midfielder Sander Berge was equally impressed by the latest landmark.
"It's madness," Berge said. "It's everyday business that Haaland scores goals, so it's reasonable that he is up there, but it's powerful."
The 26-year-old has also moved level with Brazil legend Ronaldo on 62 international goals and has now surpassed him. Ronaldo scored 62 times for Brazil before retiring in 2011.
Haaland's latest goals also put him behind only Sweden's Lotta Schelin on the overall Nordic international scoring list. Schelin scored 88 goals for Sweden's women's team.
His finishing proved decisive against Denmark, with Danish broadcaster DR analyst Michael Sten Jensen praising the striker's impact.
"Norway has him, and they should be thankful for that on a night where his sheer ruthlessness ensured the Norwegians secured the bragging rights," Jensen said.
Danish newspaper B.T. described Denmark as being "brutally punished by Norway's most dangerous man".
Denmark will have the chance to respond when they host Norway in the final Nations League group match on November 17.
Norway's next match is against Portugal on Sunday.
Netherlands manager Xavi has recalled Manchester United striker Joshua Zirkzee after Brian Brobbey was ruled out of the remainder of the international break with a muscle injury.
Jurgen Klopp was left encouraged by Germany's performance in his first match as head coach, despite seeing his side concede a late equaliser in a 1-1 draw with the Netherlands in the UEFA Nations League on Thursday.
Leeds United star Ethan Ampadu has demanded greater standards from Wales after their winless run was extended by a 1-0 Nations League loss to Portugal in Lisbon.
Rio Ngumoha believes his rapid rise into the Liverpool first team came from having the confidence to believe it could happen.
