In a frantic opening, Mohamed Elyounoussi handed Lars Lagerback's side a second-minute lead before Paddy McNair levelled after six minutes.
Haaland then fired home a wonderful side-footed half-volley from 20 yards just 67 seconds later before Alexander Sorloth added a third before the midway point of the first half.
Sorloth grabbed a second shortly after the interval, before another fine strike from Haaland after 58 minutes sealed a comprehensive defeat for Ian Baraclough in his first home game in charge of Northern Ireland.
Norway wasted little time signalling its intentions, taking the lead after just 102 seconds courtesy of Elyounoussi's superb chest control and volley from Stefan Johansen's lofted ball to the back post.
The hosts roared back only four minutes later when McNair stroked into an empty net from eight yards after Rune Jarstein had pawed away Conor Washington's effort.
Haaland promptly restored Norway's lead, though, the Borussia Dortmund striker whipping into Bailey Peacock-Farrell's right-hand post from outside the penalty area.
It extended its advantage after 19 minutes when Sorloth steered home Haitam Aleesami's wonderful left-wing cross at the back post.
Norway started the second half like they did the first, Sorloth stroking home from eight yards in the 47th minute after being selflessly teed up by Haaland, who had latched onto a long ball over the top.
Haaland then wrapped up the scoring 11 minutes later, sumptuously curling home from just inside the area after running onto Omar Elabdellaoui's headed pass.