The game started with both teams showing promise, but it wasn't until the 18th minute that the scoring began, with Phil Foden heading in a cross from Jeremy Doku to give City a 1-0 lead.
United had chances to equalize, but City's goalkeeper, Gianluigi Donnarumma, made several key saves to keep his team ahead.
Haaland's first goal came when he was played through by Doku and slotted past the onrushing Altay Bayindir, and he added a second goal shortly after when he punished sloppy play from United and slotted the ball home.
City's victory was their first win over United in five head-to-head matches, and it gave them a much-needed boost after a recent slump in form.
Haaland's performance earned him the Man of the Match award, and he was instrumental in City's victory.
The win also marked a turning point for City, who had been struggling to find their form in recent matches.