Strasburg (1-1) allowed just one hit while fanning 10 and walking two.
"I was pretty impressed," said Nationals manager Davey Johnson. "He just pitched. He didn't overthrow, he just stayed within himself and made pitches."
Ian Desmond had two RBI for the Nationals (80-81), who went 15-5 to close the season.
Drew Storen tossed a 1-2-3 ninth to earn his 43rd save of the year.
The Marlins played their final game at Sun Life Stadium, the only home they have known during their 19 seasons as a franchise.
Next season, the Marlins will relocate to a 37,000 seat, retractable roof stadium in the Little Havana section of Miami. In addition, on November 11 the club will officially change its name to the Miami Marlins.
Chris Volstad (5-13) allowed two runs on three hits over six innings to suffer the loss. He walked two and struck out five.
"The team has been around at this stadium for awhile...a lot of memories for a lot of people,' said Volstad. "To be a part of that and to kind of wrap it all up is pretty special."
Gaby Sanchez hit an RBI double for the Marlins (72-90), who dropped five of their last six games to finish dead last in the NL East
Washington took a 2-0 lead in the fifth. Ivan Rodriguez and Steve Lombardozzi began the inning with singles. Strasburg's sac bunt advanced the runners and Desmond's base hit brought them home.
Ryan Mattheus relieved Strasburg to begin the home seventh and the Marlins took advantage. Logan Morrison drew a two-out walk and Sanchez followed with a double to make it a 2-1 game. Bryan Petersen then singled off of Sean Burnett to place runners on the corners, but Brett Hayes grounded out to end the inning.
Pinch-hitter Alex Cora led off the eighth with a triple and scored two batters later on Roger Bernadina's single to give the Nationals a 3-1 lead.
Tyler Clippard tossed a scoreless home half before handing the ball to Storen in the ninth with Morrison striking out to end the game and the season for both teams.
Guillen was released from his contract with Chicago on Monday. The Marlins compensated the White Sox -- who retained their rights to Guillen -- with prospects Ozzie Martinez (infielder) and Jhan Marinez (pitcher)...Florida won the season series with Washington, 11-7.