Jimmy Rollins had four hits and Marlon Byrd doubled and drove in a pair of runs for Philadelphia. The Phillies won for just the third time in 11 games against the Nationals.
Adam LaRoche and Zach Walters homered for Washington.
The game was delayed for 24 minutes because of heavy rain, lightning and thunder after the sixth. Burnett didn't return after the weather cleared, having thrown 93 pitches.
Burnett (2-1) gave up one run on three hits while striking out seven and walking two. The right-hander had seven strikeouts to up his career total to 2,215, moving past Jim Palmer into 52nd all-time.
Tanner Roark (2-1) had the poorest start of his two-year career, allowing seven runs on seven hits in four-plus innings.
The runs and innings were career-worsts for Roark, who was making his 11th major league start.
Howard started the trouble for Roark by hitting an opposite-field, three-run homer in the first. The home run snapped Roark's scoreless streak at 18 innings.
Asche connected for a solo shot in the second to make it 4-0. Carlos Ruiz's RBI double in the fourth and Byrd's two-run single in the fifth gave Philadelphia a 7-0 cushion.
LaRoche homered in the sixth. He continued to have success off Burnett, raising his average to .400 (10-for-25) with two homers and six RBIs against the right-hander.
LaRoche, who has been slowed by a quadriceps injury, was lifted after hitting the homer.
Walters, pinch-hitting in the seventh, homered off Mario Hollands with two outs. 7-2. All three of the rookie's hits this season are homers.
NOTES: Phillies LHP Cole Hamels (0-2, 6.75) has been scratched from his scheduled start on Sunday because of the flu. Hamels will start Tuesday against Toronto. RHP Roberto Hernandez (1-1, 5.74) now will oppose Nationals LHP Gio Gonzalez (3-1, 3.25) in the conclusion of the three-game series. ... Former Phillies closer Brad Lidge threw out the ceremonial first pitch. Lidge converted all 48 of his save opportunities during Philadelphia's 2008 World Series season. ... Third-base umpire Jim Reynolds left the game after the first inning due to an undisclosed illness and was replaced by Toby Basner. ... Rollins had been hitless in his last 11 at-bats.
