The Cubs completed a three-game sweep of the Nationals, who have dropped four in a row overall.
Andrew Cashner and Carlos Marmol worked an inning each to complete the shutout. They both gave up a hit.
The game was scoreless through seven innings but Tyler Colvin drew a walk off Marquis (0-7), stole second and scored on Starlin Castro's one-out double. After Marlon Byrd struck out, Aramis Ramirez hit his 20th homer of the season.
Alfonso Soriano added a home run in the ninth, his 21st.
Marquis has lost all of his starts this season after having had a winning record in each of the last three years.