Simon (6-2) permitted just one run on five hits and a walk to improve to 5-0 in five starts away from home this season, with the effort giving the Reds their first series win in Washington since June 4-6, 2010.
The Nationals' lone score came on a leadoff home run from Denard Span in the bottom of the first.
Washington starter Tanner Roark (3-2) pitched well in a losing cause, allowing two runs -- one earned -- over six innings of work.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014