The AFC Asian Cup holders needed only two minutes to open the scoring when defender Tomoaki Makino, after exchanging straight passes with Yoshito Okubo, produced a cross from the left for Maeda to score with his head.
Japan controlled the game throughout the first half, never giving the visitors a scoring chance. Iceland played more aggressively after the break, but it was Japan who scored in the 53rd minute, with second-half substitute Kengo Nakamura passing to Jungo Fujimoto for his first goal for the national team.
In the 79th minute, Makino also scored his first goal for the national side, firing in a right-footed shot. The goal finished the game and gave Iceland's new coach, the Swede Lars Lagerback, a losing debut. Iceland saved some face when forward Arnor Smarason pulled one back in injury time from a penalty.
"It was the first game in 2012 and I wanted to start with a win. Everybody showed a good performance today, although my players were physically not in their 100 per cent," said Japan coach Alberto Zaccheroni.
"I hope that we can keep the momentum," added the Italian. Meanwhile, Fujimoto said after his first goal in 11 games: "I'm happy...For me, this is my start."
Iceland will play Norway, Slovenia, Switzerland, Albania and Cyprus in the European qualifying Group E, starting in September this year.