Iwakuma (6-1) scattered seven hits and two walks while fanning five in his outing. He lowered his earned run average to 2.13, second-lowest in the American League. Tom Wilhelmsen was perfect in the ninth to notch his 12th save.
Kendrys Morales had a two-run home run and Jesus Sucre had an RBI for the Mariners, who have won four of their last six games.
Minnesota starter Mike Pelfrey (3-6) lasted 5 1/3 innings, allowing all three runs on six hits and four walks.
"With our night offensively, I'd say their guy was pretty good," said Twins manager Ron Gardenhire. "Pelfrey matched (Iwakuma) for a long time."
Neither team was able to garner much offense, as both teams combined to record just six hits until the sixth inning.
Kyle Seager hit a leadoff single, setting up Morales' two-run shot. Raul Ibanez singled and Nick Franklin drew a walk two batters later. Anthony Swarzak came in to replace Pelfrey, but he gave up an RBI single to Sucre.
After 98 pitches, Iwakuma was taken out and Charlie Furbush got the final out of the eighth before being replaced by Wilhelmsen.
Seattle has seven shutouts this season ...Minnesota has been shut out four times ... Pedro Florimon went a perfect 3-for-3 with a double ... Morales has three home runs and 14 RBI over his last 11 games ... Right-handed hitters are 1-for-37 against Wilhelmsen this season.
06/01 03:55:09 ET