Iwakuma (2-0) won his second straight start after allowing just four hits with seven strikeouts and no walks. Fernando Rodney spun a scoreless ninth for his 10th save of the season.
Seattle made the most of its opportunities after producing just two hits. Corey Hart drove in the game's lone run and Mike Zunino's double accounted for the team's only other hit.
The Mariners have won six of their last seven games and nine of their last 11.
Kansas City's offense didn't fare any better. Eric Hosmer supplied two of the Royals' four hits.
Danny Duffy (1-3) was tagged with the loss after allowing just one run on two hits with three walks and four strikeouts across six-plus innings for the Royals, who have lost six of their last eight.
Seattle scored the only run in the third. Zunino doubled to center field to lead off and moved to third on Michael Saunders' sacrifice bunt. Two batters later, Robinson Cano was intentionally walked before Hart singled on a line drive to center to score Zunino.
Rodney came on to pitch the ninth for Seattle. He issued a leadoff walk to Alcides Escobar, who moved to second on Norichika Aoki's sacrifice bunt. Rodney walked Hosmer before striking out Billy Butler and getting Salvador Perez to ground into a fielder's choice to end the game.