Griner, last year's first overall draft pick, made her first seven shots and finished with five blocks. Her first miss came in the fourth quarter with the game well in hand.
''Glad to beat the Storm, finally,'' Griner said, referring to the Mercury's five straight losses to Seattle dating to last season. ''It was important for me to be patient. I know if I get my shot blocked a couple of times, I would definitely not try to take it all the way all the time.''
The Storm tried early to take the ball at Griner, who was foul-prone at times as a rookie, but soon saw that the strategy was futile.
''I think she's getting comfortable in the league,'' Storm forward Camille Little said of Griner. ''She was more mobile, defensively and offensively.''
The Mercury went 6 of 9 from 3-point range in the first half and never trailed.
DeWanna Bonner scored 11 points and guard Anete Jekabsone-Zogota came off the bench to hit all four of her shots, including three 3-pointers, and also finished with 11 points.
The Mercury led by as many as 22 points and shot 61 percent in the first half, while holding Seattle to 34 percent shooting.
''The key stat for me was we kept this team to 34 percent. Our goal is to hold teams to 40 percent,'' Mercury first-year head coach Sandy Brondello said. ''We can still get better.''
Little had 14 points for the Storm, coming off a home loss to Los Angeles on Friday night in their opener. The Storm trailed 46-30 at halftime and got only as close as 12 points in the third quarter.
Seattle coach Brian Agler missed the game to attend his son's college graduation. Assistant Jenny Boucek guided the team in his place.
The Mercury take on Los Angeles Sunday night on the road in the second of back-to-back games.