The City striker scored all three goals in their first game of the international break with fellow City team-mate Oscar Bobb also named in the starting 11.
It took Haaland just 15 minutes to put his nation ahead after he nodded home David Wolfe’s cross.
The second half was a much closer affair with Norway finding it difficult to break through Kosovo’s defensive line.
But the City number nine was there again on 70 minutes to double Norway’s lead before putting the game out of reach for Kosovo five minutes later with a third.
The trio of goals puts Haaland’s tally to 30 goals in 32 games for Norway.
Bobb, deployed on the right, proved to be quick and tricky for Kosovo and put in another strong performance for his country before being substituted in the 62nd minute.
Norway’s next assignment will see them take on Denmark on Saturday 8 June.
Elsewhere, Kevin De Bruyne captained Belgium in their friendly triumph over Montenegro.
In his 100th appearance for his nation, the midfielder fired the Red Devils ahead in the 44th minute after a convincing first half performance.
And it would prove to be his last contribution as he was substituted at half-time. The break also saw his City team-mate Jeremy Doku took to the pitch for the remainder of the second 45 minutes.
Leandro Trossard converted from the penalty spot in added time to seal their 2-0 win.
Belgium will be in action again before EURO 2024. They will take on Luxembourg on Saturday 8 June.
