The hosts overwhelmed helpless Oman, who were only able to avoid a bigger loss thanks to the tireless efforts of Wigan goalkeeper Ali Al-Habsi throughout the match
The Samurai Blue opened their account for this round with a 12th-minute strike by Keisuke Honda, following the CSKA Moscow man's goal up with second-half efforts by Ryoichi Maeda and Shinji Okazaki.
"As the first match of the round it was an important victory and great for our morale," Zaccheroni told reporters immediately after the match.
"We were focused and I want to again thank the supporters who cheered us and motivated us throughout the game.
"I hope they'll all come to the [June 8] match against Jordan. With this kind of support we’ll win again!"
Keisuke Honda, who returned to action in last week’s Azerbaijan friendly after a nine-month post-surgical recovery period, also had plenty to smile about after his first international goal since last August.
"I hadn't scored in a while so I was definitely looking for a goal," the 25-year-old said of his half-volley from Yuto Nagatomo's cross. "I think we were able to relax after we scored so early.
"Now we have to prepare in order to win our next game as well."
Team captain Makoto Hasebe praised his team-mates, but despite dominating possession felt that his squad could have done more.
"I'm very relieved. We did well by scoring early in both halves, but I think we could have scored two or three more goals," the Wolfsburg midfielder reflected.
"We're not yet at 100 per cent but now we have four days to get ready for the next match."