The result ended a 28-year absence from the World Cup for Norway, who led at the break despite a spirited response from their opponents. Haaland broke the deadlock in the 29th minute, arriving at the back post to convert a low cross from David Moller Wolfe.
Iraq levelled ten minutes later through a powerful header from Aymen Hussein, meeting a cross from Amir Al Ammari. Haaland restored Norway's lead before half-time, pouncing after Iraq goalkeeper Jalal Hassan hesitated over a back pass and turned the ball into his own forward's path.
Leo Ostigard extended the lead in the second half, before a stoppage-time own goal from Hussein completed the scoring.
Iraq coach Graham Arnold struck a defiant tone despite the heavy defeat, pointing to the bigger picture of the group stage.
"Look, three points will get you through to the next phase, and we've got two more games to go. Great performance at times, but a couple of mistakes hurt us badly."
Norway move level with France on three points in Group I after the opening round of matches. Iraq face France in their next group fixture, while Norway are next due to meet Senegal.