Haaland took his tally for the national team to 64 goals in 56 appearances, eclipsing Ibrahimovic's 62 goals in 122 matches for Sweden.
The Manchester City striker completed his double in the 74th minute, sealing Norway's first competitive victory over Denmark.
"It is not possible to explain, nor is it possible to learn. He is born with it. It is instinct," Norway manager Stale Solbakken said.
Haaland, who made his senior international debut in 2019, has scored at a rate of more than 1.1 goals per game for Norway.
"It's madness," Norwegian midfielder Sander Berge said. "It's everyday business that Haaland scores goals, so it's reasonable that he is up there, but it's powerful."
More goals than Brazil's Ronaldo
The 26-year-old also moved past Brazil great Ronaldo, who scored 62 international goals before retiring in 2011. Former Sweden women's forward Lotta Schelin holds the overall Nordic international record with 88 goals.
Haaland's clinical finishing dominated the reaction in Denmark.
"Norway has him, and they should be thankful for that on a night where his sheer ruthlessness ensured the Norwegians secured the bragging rights," Danish broadcaster DR analyst Michael Sten Jensen said.
Danish newspaper B.T. wrote that Denmark were "brutally punished by Norway's most dangerous man."
Denmark striker Rasmus Hojlund acknowledged the unique threat posed by the forward.
"Erling has a way of finding the path to the goal," Hojlund said. "So in that sense it comes as no surprise, but at the same time it frustrates me."
Denmark will have a chance for revenge when they host Norway on the final matchday of the Nations League group stage on November 17.