Blanton (10-7) allowed five hits and struck out seven. The Phillies were one out away from recording three consecutive shutouts for the first time in 40 years when Willie Harris singled in a run off Tyler Walker.
"Hitting is contagious, but pitching is contagious, too," Blanton said. "You see a lot of quality pitches and a lot of outs and it gets in your head. It breeds confidence."
The NL East-leading Phillies reduced their magic number for clinching their third straight division title to 11 with 18 games remaining.
Livan Hernandez (8-11) allowed two runs and seven hits in six innings. The lowly Nationals are 3-14 against Philadelphia this season.
Frustrated by another sloppy performance, manager Jim Riggleman held a team meeting after the game.
"We made too many mistakes," Riggleman said. "A lot of bad things happened that we can't continue to allow. We've got to do a better job of handling the details of the game."
Utley singled with two outs and moved to third on Howard's base hit. Howard then broke for second and slid in safely ahead of catcher Wil Nieves' throw. Utley raced home once Nieves released the ball and scored without a throw as shortstop Cristian Guzman reacted slowly after applying the late tag.
It was Howard's seventh stolen base this season. He had two career steals before this year, but dropped more than 25 pounds in the offseason.
"I think he's a little quicker because of the weight," manager Charlie Manuel said.
Utley became the 10th player in franchise history to record 20 steals and 20 homers in the same season.
Werth drove a 1-2 pitch from Jason Bergmann deep to left-center in the seventh for his third career slam and second this year. The All-Star right fielder has 34 homers and 88 RBIs in his first full season as a regular.
"I knew he could produce from an offensive standpoint and I knew he had power, but I didn't know how consistent he'd be," Manuel said. "He's still learning. He can get better."
Phillies RHP Chan Ho Park left with a strained right hamstring after pitching a scoreless eighth inning. ... Philadelphia had four straight shutouts from Aug. 13-16, 1969, according to STATS LLC. ... Phillies LHP J.A. Happ will make his first start since Sept. 2 on Friday at Atlanta. The rookie has been sidelined with an oblique injury. ... Phillies LHP J.C. Romero (elbow) was encouraged by a bullpen session and hopes to return next week. Romero said he'd like to make five relief appearances before the postseason. ... Utley has stolen 23 straight bases, including two last season. ... Nationals C Jesus Flores had surgery to repair a torn labrum in his right shoulder. He's expected back by the middle of spring training.