In the opener, Tommy Milone threw six scoreless innings and pinch-hitter Ryan Zimmerman delivered an RBI single in the 10th to lift the Nationals to a 4-3 victory.
Detwiler (3-5) allowed three hits in his longest career outing. The left-hander earned his first road win after going 0-9 in his first 12 starts away from home.
Lee (16-8) gave up three runs - two earned - and 11 hits, striking out nine in seven innings. It was his first loss since July 25.
The slumping Phillies have lost four straight since clinching their fifth consecutive division crown. It ties their longest losing streak of the season, previously done twice. They have been resting many of their regulars, however.
The Nationals have won nine of 12.
Henry Rodriguez got the last two outs in the eighth and Drew Storen finished off the three-hitter for his second save of the day and 40th in 45 chances this season.
Danny Espinosa hit his 20th homer to give the Nationals a 1-0 lead in the second.
Detwiler helped himself with a two-out RBI single in the sixth. He was 2 for 41 lifetime before hitting a liner to center to score Espinosa, who singled with one out.
The Nationals got an unearned run in the seventh when catcher Carlos Ruiz tried to pick off Jayson Werth at third, but hit him in the arm with the throw. Werth, who led off the inning with a double, scored when the ball bounced into foul territory. Werth left the game with a bruised right elbow.
The Phillies haven't given Lee much support in his losses this season, scoring just 14 runs in those eight games.
Lee has allowed four earned runs in his last three starts but is 0-1 with two no-decisions.
The lack of run support could cost Lee a chance at the NL Cy Young Award. Lee, teammate Roy Halladay and Los Angeles Dodgers lefty Clayton Kershaw are considered the top three candidates.
Milone, the organization's 2010 minor league pitcher of the year, picked a perfect time to set career highs in innings and pitches (93). The left-hander allowed four hits, struck out two and walked none.
"I was moving the ball in and out," Milone said. "It was actually pretty easy. Some days, you go in and out when you're trying to throw strikes. Today, it seemed a lot easier."
Pinch-hitter Michael Morse sparked Washington's winning rally with a two-out walk in the 10th. He moved up on a passed ball and scored when Zimmerman singled to center off Michael Stutes (6-2).
Tom Gorzelanny (4-6) worked the ninth for the victory. Storen got Ross Gload to ground out with runners on first and second to end the game.
The Phillies started two regulars - Shane Victorino in center and Hunter Pence in right - in the first game. Both were pulled by the seventh inning.
Roger Bernadina hit a three-run homer off reliever Michael Schwimer in the seventh for a 3-0 lead.
"I was looking for a pitch and he left one out over the plate," said Bernadina, who tied his career high with three RBIs. The Phillies tied it in the bottom half when Raul Ibanez hit a three-run drive to right on an 0-2 pitch from Tyler Clippard. It was Ibanez's second career pinch-hit homer, the last one coming in 2001 for Seattle.
Kyle Kendrick bolstered his case for a spot on the Phillies' postseason roster with his second consecutive strong outing. He pitched six scoreless innings.
"He's been good, very good," Phillies manager Charlie Manuel said. "He finds a way to get it done."
Kendrick has given up three or fewer earned runs in each of his last nine starts.
"I feel pretty good right now," Kendrick said. "I have good command of my pitches."
NOTES: Phillies 1B Ryan Howard missed both games. He's been nagged by bursitis in his left foot. ... The Phillies reached 215 straight sellouts at Citizens Bank Park, including postseason play. ... Espinosa has a nine-game hitting streak. He's 7 for 10 off Lee, including three homers. ... Nationals reliever Ryan Mattheus, who missed the last 22 games with a right shoulder strain, was activated from the 15-day DL. ... Rookie Vance Worley (11-2) faces Washington's John Lannan (9-13) on Wednesday night.