Oswalt (6-13), a former 20-game winner acquired from Houston in a four-player trade Thursday, allowed five runs - four earned - and seven hits in six innings. He walked two, struck out four and hit two batters.
It was another tough start against Washington for the right-hander, who lasted only 2 1-3 innings, yielded four runs and was ejected for arguing balls and strikes when he faced the Nationals in Houston on May 31.
Stammen (3-4) went 6 1-3 innings, and gave up one run and five hits. He walked one and struck out five.
Jayson Werth homered for the Phillies.
Adam Kennedy had a season-high four hits for the Nationals, who have won three of four.
Nyjer Morgan led off the Washington first with a triple and scored on Kennedy's groundout for a 1-0 lead.
Phillies catcher Carlos Ruiz's throwing error set the stage for two runs in the Nationals third. Stammen singled, Morgan was hit by a pitch and Kennedy tried to bunt the runners over. Ruiz pounced on Kennedy's bunt single and threw to third, but third baseman Greg Dobbs had left the base uncovered to charge the bunt and Ruiz's throw sailed into left field.
Stammen scored and Morgan went to third on the error. Ryan Zimmerman hit a sacrifice fly for a 3-0 lead.
Josh Willingam doubled in two runs in the fifth after Kennedy doubled and Oswalt hit Adam Dunn with a pitch.
Werth led off the Phillies seventh with a solo shot to left, his 15th homer of the season.
In the Washington seventh, Roger Bernadina hit a two-run, bases-loaded double and Ian Desmond hit a sacrifice fly.
NOTES: Philadelphia SS Jimmy Rollins returned to the lineup after missing three games with a bruised left foot. ... Nationals manager Jim Riggleman said he would employ a closer-by-committee approach following the trade of RHP Matt Capps to Minnesota on Thursday night. ... RHP Stephen Strasburg, who was scratched from Tuesday's start and placed on the 15-day DL on Thursday with right shoulder inflammation, will play catch in the outfield either Saturday or Sunday, Riggleman said. ... Oswalt had a forgettable first at-bat as a Phillie. Bernadina charged what might have been a single to right and threw Oswalt out at first. ... Philadelphia's Placido Polanco went 0 for 4, ending a 24-game hit streak against Washington. It was the longest active streak against an opponent in the majors.