"It was one of those things where I took one good swing all night out of four at-bats, but it worked," Byrd said of his home run off Doug Fister (10-3).
His heroics came one day after his general manager expressed surprise teams weren't more aggressive in pursuing Byrd, who's hitting .271 with 21 homers.
"It feels good to be wanted (here)," Byrd said. "But at the same time Ruben (Amaro) was probably like, `hey this is my guy, you're going to have to do something big for me to pull the trigger."
Hernandez (6-8) allowed an unearned run on five singles. He retired the last 10 batters he faced and 17 of the last 18. Over his last four starts, Hernandez is 3-0 with a 1.88 earned run average, including two wins against Washington while allowing no earned runs over 15 1/3 innings.
"There were some hard hit balls. Some good plays behind him," Phillies manager Ryne Sandberg said. "But he was aggressive in the strike zone and stayed ahead of the hitters."
The Nationals hit numerous line drives that ended up in Philadelphia gloves.
"We wish we could steer it," Nationals manager Matt Williams said. "I think Susan Sarandon said it, `Hit it where they ain't.' We didn't do a very good job of that tonight."
Hernandez himself made a stellar catch off a smash at him by Denard Span in the eighth.
"I don't know how I caught that ball," he said.
NL-East leading Washington has lost four of five.
Fister took his first loss since June 15, allowing two runs and six hits in seven innings. He has allowed three runs or fewer in 13 of his 15 starts.
The Phillies took the lead in the second. Sizemore hit a deep drive and Harper raced back, got a glove on it at the warning track, but didn't make the catch. Sizemore got a double and scored on Asche's single.
Washington tied it in the bottom of the inning after an error. Adam LaRoche hit an infield pop-up. Hernandez and third baseman Asche had a play on it, but the ball dropped between them.
Asche threw wildly to first, allowing LaRoche to go around to third. Ian Desmond then bounced a singled, scoring LaRoche.
Phillies: Cliff Lee was placed on the 15-day disabled list with an elbow strain and the team recalled left-hander Cesar Jimenez from Triple-A Lehigh Valley. Lee will be examined by the team doctor Saturday. Sandberg said he was considering starting left-handed hitting outfielder Dominic Brown against righty Fister, but Brown was suffering from a sore throat and fever.
Washington's Jordan Zimmermann (6-5, 3.17) makes his fifth try for his 50th career win Saturday. He allowed four runs over 3 1/3 innings in loss at Philadelphia on July 11. A.J. Burnett (6-10, 4.15) looks to rebound from last start, when he allowed seven runs in five innings against the New York Mets on Monday. His last win came July 11 against the Nationals and Zimmermann.
Washington's Denard Span has reached base safely via hit or walk in 27 straight games. ... Philadelphia's Ben Revere extended his hitting streak to seven games.
Cabrera, acquired in a trade Thursday with Cleveland, went 0 for 4 in his debut. Starting his first game at second base since 2009, he made a nice sliding stop of Jimmy Rollins' grounder on the right field grass, rose, spun and threw out the speedy Rollins.