Suzuki connected off Yomiuri reliever Levi Romero to give Oakland a 3-0 lead and Jemile Weeks added an RBI single to make it 4-0. Coco Crisp later drew a bases-loaded walk to make it 5-0.
"It went out like a bullet," Suzuki said of his home run. "I hit the ball pretty well so it felt really nice."
Milone allowed two hits in five innings and struck out seven to pick up the win.
Milone is one of several young pitchers vying for a spot in Oakland's rotation and improved his chances with Sunday's solid outing at the Tokyo Dome.
"My fastball was very good and the changeup as well," Milone said. "I was just throwing strikes and trying to keep them low. Everything was working good."
The Athletics are in Japan to open the 2012 season against the Seattle Mariners on Wednesday and Thursday.
The A's took a 1-0 lead in the top of the second when Weeks singled to right to score Josh Reddick from third.
This will be the fourth Japan opener, following the New York Mets and Chicago Cubs (2000), the New York Yankees and Tampa Bay (2004), and Boston and Oakland (2008).
Major League Baseball and the players' association said the series also will aim to assist rebuilding in Japan following last year's earthquake.
On Tuesday, a group of players will travel to Ishinomaki in the disaster-hit northeast region to conduct a baseball clinic.
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