Ryoichi Maeda steered in a point-blank header in the 25th minute for the Asian champions, who lost playmaker Shinji Kagawa to a back strain an hour before kick-off.
"It's three points, we'll take it," Japan coach Alberto Zaccheroni told reporters. "It was an important result. We want to qualify for Brazil as quickly as possible."
Iraq, shock Asian Cup winners in 2007 and now under the stewardship of former Japan coach Zico, could have scored twice before Maeda struck.
The Brazilian's young side came agonisingly close to silencing the crowd of 60,000 in Saitama, both times having close-range efforts blocked.
Those misses proved costly as a quickly-taken throw-in released Shinji Okazaki, whose first-time cross was turned in by Maeda.
"We practised that move," said Maeda. "Oka's pass was perfect and I just had to get on the end of it. It was down to him. We knew we had to win but we still have to improve."
A diving header from Keisuke Honda, brilliantly tipped against the post by goalkeeper Noor Sabri, almost doubled Japan's lead in the second half.
Japan opened up an eight-point lead in World Cup qualifying Group B from Iraq, Australia and Oman, before Jordan hosted the Socceroos later on Tuesday.
"We have the quality to cover the holes if we lose one or two players," Japan captain Makoto Hasebe said of Kagawa's late pullout, which will be of concern to Manchester United.
"The teamwork was excellent and we got the three points we wanted but we can play better. We know there are some difficult games away waiting for us."
Japan, who have played at every World Cup since first appearing in 1998, have 10 points after four matches in the final round of Asian qualifying.
- Ryoichi Maeda
- Shinji Kagawa