The Borussia Dortmund star, 20, has now tallied six goals in as many international matches. He has now scored 51 goals in 48 games for club and country.
The win at Oslo's Ullevaal Stadium provides some relief for Norway after they were eliminated from the Euro 2020 playoffs by Serbia last Thursday.
Haaland's hat trick came 10 minutes later with a rising screamer that hit the top of the net from just inside the box. Following the match, he was quick to call out Odegaard for his efforts in the win.
"It's nice to play with Odegaard. It will only get better in the years to come. We are still young," Haaland told Norweigan outlet TV2.
Odegaard returned the compliment to what could become one of top attacking duos in international play.
"He starts perfectly every time and almost never goes offside. He times it well and always gets there first," Odegaard said of his compatriot.
Norway share the Group B1 lead with Austria with six points after three matches, with the latter defeating last-place Northern Ireland 1-0 in Belfast. Romania go to third place with four points.