Lee (3-7) broke a personal four-start winless streak with the strong performance, during which he yielded one run on seven hits. The left-hander didn't issue a walk and struck out five.
Lee also helped himself at the plate. With one on and one out in the fifth, the pitcher laced a 1-1 pitch over the head of Nationals center fielder Bryce Harper, scoring Kevin Frandsen.
Jimmy Rollins followed by smashing a two-run homer to ice the contest.
Laynce Nix added a solo shot and Josh Lindblom collected his first career save as the Phillies completed a three-game series sweep.
Nats starter Jordan Zimmerman (9-8) was touched for three runs on five hits in a five-inning effort.
Tyler Moore supplied the only RBI for National League East-leading Washington.