Strasburg (11-10) went 7 2-3 innings and struck out eight, increasing his NL-leading total to 210. The right-hander also broke the Nationals' single-season record of 207 set by Gio Gonzalez two years ago.
Former Mariners reliever Rafael Soriano worked around two ninth-inning singles to earn his 30th save in 35 attempts for the NL East leaders.
Dustin Ackley's home run chased Strasburg. Ackley was drafted No. 2 overall in 2009 directly behind the Washington phenom.
Werth gave the Nationals an early lead with a two-run homer in the first off Roenis Elias, who got the ball after Chris Young was pushed back to Monday. Elias (9-12) recovered to last six innings for the first time since June 28. He allowed three runs two earned and six hits.
Seattle threatened in the ninth when Kyle Seager and Endy Chavez singled, but Soriano retired James Jones on a game-ending grounder.
Anthony Rendon had an RBI single in the fifth for the Nationals.
Strasburg pitched out of trouble on multiple occasions. In the third, he left runners on second and third by throwing a called third strike past Robinson Cano for his first strikeout. Strasburg also stranded runners at the corners in the fifth by fanning Ackley.
Strasburg, who walked none, has allowed one run in three of his past four starts.
Mariners: Interim manager Trent Jewett said OF Chris Denorfia (stiff neck) is a little banged up, but was available off the bench.
Nationals: Despite hitting two home runs Friday, catcher Wilson Ramos did not start behind the plate. Washington manager Matt Williams said that was partly to lighten the workload for Ramos and limit the wear and tear on him. Ramos was the DH.
Mariners RHP Hisashi Iwakuma tries to bounce back in the series finale Sunday after allowing five runs over 2 1-3 innings at Boston in his most recent start.
Nationals RHP Tanner Roark looks to allow three runs or fewer for the fifth straight start.