The Cuban defector crunched a line drive to left centre in the bottom of the seventh for his first home run in the majors after Justin Smoak had blasted a solo homer in the top of the inning to give Seattle the lead.
Josh Reddick added an insurance run with a towering shot to the right-field seats on the next pitch and Jonny Gomes tacked on another in the eighth with a long ball to centre field.
"That was a big, big hit and I'm so happy to hit a home run," Cespedes, billed as one of the best players to come out of his country in a generation, said in a field interview.
"It was like a dream come true. I dedicate that homer to everyone in Japan."
The A's were beaten 3-1 in extra innings in Wednesday's curtainraiser, extending MLB's longest active opening-day losing skid to eight years, the worst since 1992.
Bartolo Colon picked up the victory for Oakland, pitching eight innings, limiting Seattle to one run on three hits, with six strikeouts.
"He's the perfect guy to pitch after we lost a tough game last night," said A's manager Bob Melvin. "I'm not sure he has a pulse. My heart was beating a lot faster than his was."
Reliever Shawn Kelley took the loss for Seattle.
Ichiro Suzuki, whose four hits had sparked Seattle the previous evening, went 0-for-4, the crowd of 43,000 letting out a loud groan when his last swing bobbled to first baseman Kila Ka'aihue.
"It was great to get the win," said Colon. "To be able to keep Ichiro in check - one of the world's best players - was a great feeling."
Seattle, who had the worst offensive record in the majors last season, left the bases loaded at the top of the fifth and paid for it, despite taking the lead through Smoak.
"We didn't execute pitches," said Mariners manager Eric Wedge. "We were one pitch away from really being in command of the ball game late.
"But then Shawn hung that slider...so big ball (important pitches) really hurt us late in the ball game."
The two teams were scheduled to meet in Tokyo in 2003, but the series was called off because of the threat of war in Iraq.