Suzuki then gave Seattle an insurance run with a single to center off Oakland reliever Jerry Blevins that scored Ackley from second.
The capacity crowd of 44,227 at Tokyo Dome was a sea of flashbulbs every time Suzuki came to bat. He got a standing ovation when he took his position in right field in the final inning.
Suzuki got his first hit in the first inning on a grounder over the mound that was deflected by Oakland starter Brandon McCarthy, allowing Suzuki to beat out the throw from shortstop Cliff Pennington.
Ackley put the Mariners ahead 1-0 in the fourth on a solo homer to center off McCarthy. Suzuki then came up and beat out a grounder to short for his second hit of the game.
"I'm glad I was able to put our team on the board and get an early lead," Ackley said.
Oakland tied the game in the bottom half of the inning when Kurt Suzuki hit a double to left that scored Pennington from third.
Seattle reliever Tom Wilhelmsen picked up the win after pitching two scoreless innings in the ninth and tenth. Brandon League retired the side in the 11th for the save. Andrew Carignan took the loss after giving up both runs in the 11th.
Seattle starter Felix Hernandez struck out six and gave up one run on five hits over eight innings while walking none. McCarthy gave up one run on six hits in seven innings with three strikeouts and no walks.
Cuban defector Yoenis Cespedes picked up his first major league hit with a double to lead off the seventh.
When the game started, it was 3:09 a.m. on the West Coast.
The game Wednesday was 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).
Before the game, a video presentation honoring the victims and survivors of the March 11 earthquake and tsunami was played on the center field screen at Tokyo Dome. The video was narrated by Derek Jeter, Bobby Valentine and Cal Ripken Jr.
Bartolo Colon is scheduled to start Thursday's game for the A's, while Jason Vargas is set to take the mound for the Mariners.