The win completed a four-game sweep for Tampa Bay over the Mariners. The Rays are a major-league best 18-8 after having won 13 of their last 15.
Niemann (2-3) gave up seven hits and three runs over 5 2/3 innings. He walked two and struck out five. Jake McGee added 2 1/3 innings of no-hit relief and Fernando Rodney pitched the ninth for his ninth save. The nine saves are tied for the most in the majors.
The Mariners scored twice in the second with Mike Carp and Justin Smoak driving in the runs.
But the Rays got to Seattle starter Kevin Millwood (0-3) for four runs in the bottom of the inning as Jeff Keppinger hit a two-run home run and Desmond Jennings had a two-run triple.
Back-to-back doubles by Dustin Ackley and Ichiro Suzuki in the fifth accounted for the other Seattle run.
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