Washburn (1-0) gave up five hits in eight scoreless innings with a walk and four strikeouts.
The game's lone runs scored on singles by Adrian Beltre and Rob Johnson in the first and ninth innings, respectively.
Beltre and Wladimir Balentien each had two of the Mariners' eight hits.
Seattle had lost two in a row since winning the season opener Monday.
Brendan Harris had two of Minnesota's five hits.
Losing pitcher Glen Perkins (0-1) gave up an earned run and five hits in eight innings with two walks and four strikeouts.