Strasburg (11-10) struck out eight and scattered six hits for the Nationals, who have won the first two games of the set on the heels of a three-game slide.
Seattle put runners on the corners with two outs in the ninth, but Rafael Soriano induced a game-ending groundout off the bat of James Jones to notch his 30th save of the year.
Jayson Werth smacked a two-run homer, while Jose Lobaton went 3-for-4 with a run scored in the triumph.
Roenis Elias (9-12) allowed three runs -- two earned -- on six hits and two walks over six frames for Seattle, which has dropped three straight. Dustin Ackley homered in defeat.
The Nationals opened the scoring with a pair of runs in the first and added another in the fifth.
Denard Span reached on an Austin Jackson error in center to start the game and Werth stepped up two batters later and launched his two-run shot into the second deck in left.
In the fifth, Lobaton hit a one-out single, and Anthony Rendon lined a double to center two batters later to bring home Lobaton and give the Nats a 3-0 advantage.
Ackley cracked his solo shot with two outs into the front row of seats to right in the eight to get the Mariners on the board.