Since allowing eight earned runs on opening day, Lee has surrendered just eight in his last six starts. In seven innings against the Nationals, he allowed two runs, one earned.
"It is disappointing for Cliff to do his job and to get to the eighth inning and not shut them down," manager Ryne Sandberg said.
Former Phillie Jayson Werth still gets soundly booed, but he had the fans cheering after an error that led to three unearned runs in the first inning.
Werth dropped a Marlon Byrd fly ball in foul territory in the right-field corner. Byrd then crushed Stephen Strasburg's next pitch, a 96-m.p.h., four-seam fastball, for a three-run homer to right-centerfield.
"He just gave me another crack at it, and I put a good swing on the ball," Byrd said of Werth's miscue.
Washington started its comeback in the third inning, when leftfielder Tyler Moore, who entered the game batting .174, hit a solo home run to left.
Moore led off the fifth inning with a single and advanced to second when Chase Utley booted a potential double-play ball from Jose Lobaton, putting runners on first and second.
After committing 13 errors in their first 13 games, the Phillies made just one in their next 13 before Friday.
Strasburg sacrificed the runners to second and third, and Denard Span grounded out to Utley to knock in the second run.
As he returned to the dugout, Denard exchanged words with Lee, and both benches quickly emptied. There was a lot of talking, but no punches were thrown.
Span was upset about an inside pitch thrown during the at-bat. He had unsuccessfully requested a time-out and then had to elude the pitch.
"I made a pitch, and he was in the box and wasn't ready," Lee said. "I'll do that every time."
After order was restored, Anthony Rendon lined out to Utley to end the inning.
Span started the game-winning rally by leading off the eighth with a double off Adams, who relieved Lee. The centerfielder stole third and scored on Rendon's single up the middle. Werth followed with a single up the middle that just eluded a diving Jimmy Rollins, putting runners on first and second with no outs.
Washington took a 4-3 lead when Adam LaRoche drilled an RBI single up the middle against reliever Jake Diekman.
LaRoche, a lefthanded batter, had struggled against Lee, striking out twice and hitting into a double play. Couple that with the fact that lefthanded batters were just 2 for 17 against Diekman entering the game, and that was a clutch hit by the Nationals first baseman.
It would only get worse.
Ian Desmond hit an RBI double to right, as Byrd dove for the ball but failed to make the catch.
Nationals closer Rafael Soriano, who has not allowed an earned run in 11 innings, walked Carlos Ruiz to open the ninth. Cody Asche then hit into what was ruled a double play. His grounder was fielded by second baseman Danny Espinosa, who got the force at short. Desmond threw wildly to first.
Ruiz, however, was called for runner's interference.
Freddy Galvis ended the game with a pop-up, making him 1 for 31 on the season.