It was the 56th and 57th international goals for the Manchester City striker and came in Norway's first appearance in the tournament since reaching the round of 16 at the 1998 World Cup in France — two years before Haaland was born.
Leo Ostigard added the third goal in the 76th minute off a corner kick from Martin Odegaard before Kristian Thorstvedt scored a fourth just before the final whistle off Haaland's assist.
Iraq, coached by former Socceroos boss Graham Arnold, briefly equalised just nine minutes after Haaland's first strike on a goal through Aymen Hussein.
But Haaland put the Norwegians in front for good just before halftime in Boston on Tuesday (Wednesday AEST) when he snuck in front of a poor back pass to Iraq goalkeeper Jalal Hassan. Haaland beat him to the ball, pre-empting his attempted clearance, and then used his shin to put the ball in the back of the net.
Haaland's first goal came in the 29th minute, off a cross into the box from David Moller Wolfe which Haaland finished off with his right heel.
Iraq, playing in the World Cup for just the second time after debuting in 1986, held their own with a sizeable contingent of supporters that were mostly concentrated behind one of the goals.
That energy helped Iraq briefly get back into the game.
It came in the 38th minute when Amir Alammari crossed over three Norway defenders, allowing Hussein to head powerfully beyond diving goalkeeper Orjan Nyland to even the score at 1-1.
It was Hussein's 34th international goal, which includes his winner against Bolivia in Iraq's final World Cup qualifying match in April that gave the country the final spot in the 48-team tournament field.
"I thought the boys did exceptionally well first half, a couple of mistakes hurt us badly," Arnold told the BBC.
"What a great occasion this has been for Iraq. So many fans here and a great atmosphere, so it's a special night."
With PA>
