Strasburg (1-1), who missed all but the last month of the season following arm surgery, earned his first win since the injury in the season's final game, yielding only on hit while fanning 10 and walking two.
Three Nationals relievers teamed up to limit the Marlins to one run over two innings and Drew Storen tossed a 1-2-3 ninth for his career-high 43rd save as Washington won the final game to be played at Sun Life Stadium.
The Nationals took the rubber match of their season-ending, three-game series and finished 80-81, good for third in the National League East.
Florida ended its season in the NL East basement at 72-90.
Chris Volstad (5-13) lost despite yielding only two runs on three hits over six frames as the Marlins bid farewell to their home since their 1993 founding -- a football stadium built for the Miami Dolphins.
The team, which Wednesday introduced Ozzie Guillen as its manager for next year, will begin play in April as the Miami Marlins in a new baseball-only stadium.