Mohamed Elyounoussi gave Norway the lead in the second minute but, after Paddy McNair equalised, Haaland got the goal of the game with an emphatic half-volley from the edge of the box that had keeper Bailey Peacock-Farrell rooted to the spot.
Alexander Sorloth made it 3-1 when he scored from a cross at the far post and the striker doubled his tally two minutes after the restart when Norway launched a counter-attack and Haaland forced his way through to lay it on a plate for a simple tap-in.
Haaland then got his second by completing a fine move in which the ball moved up the pitch with precise one-touch passes for the 20-year-old hitman to curl it into the top corner.
Steven Davis equalled goalkeeper Pat Jennings' record of 119 caps for Northern Ireland but it was a match to forget for the captain as they dropped to the bottom of the group with no wins following their 1-1 draw with Romania last week.
The Romanians top League B Group 1 on four points with Norway third after losing their first match 2-1 to Austria who are one place above them but also have three points.