The Mariners snapped a three-game skid, scoring all its runs in the first inning to hand Texas starter Yu Darvish his first loss of the season.
Seattle pitching silenced the Texas bats with the line run for the Rangers coming on an Ian Kinsler homer in the fourth.
Iwakuma (2-0) walked one and struck out six. Tom Wilhelmsen worked a perfect ninth for his fourth save.
Darvish (2-1), who came within one out of a perfect game in his first start of the season, hit a batter and threw a wild pitch in the first inning. Raul Ibanez singled in one of the Seattle runs and Kyle Seager delivered the other two with a double.