The Nationals took a 5-0 lead through two innings, but had only a one-run advantage heading into the ninth. They picked up three insurance runs in that inning on a two-RBI single from Jayson Werth and Harper's double.
Washington maintained a four-game lead over Atlanta at the top of the National League East with seven to play.
The win went to John Lannan (4-0), who gave up five hits and two runs over 5 1/3 innings.
Jimmy Rollins hit his 23rd homer for the Phillies, who have lost three out of four.
Kyle Kendrick (10-12) lasted only two-plus innings in the loss. He was roughed up for five runs on five hits.
Ray Liotta sues skin care company over use of likeness
Millions of Getty images now available for free via embed tool