Strasburg (13-5) overcame four walks and struck out six, giving him 166 for the season, while lowering his ERA to 2.90 as the Nationals took the first of a three-game series and improved to a major league-best 70-43.
Steve Lombardozzi went 4-for-5 with four runs scored and Jayson Werth added three hits, including a two-run double, as the Nationals pounded out 11 hits.
Arizona's Trevor Cahill (9-10) was touched for four runs on six hits over six full frames.
Chris Johnson drove in the Diamondbacks' only run.
Notable deaths of 2014 [PHOTOS]