The Nationals have nine comeback wins in 29 games.
"It's a bunch of guys who are not going to quit," Strasburg said.
Benches and bullpens emptied in the fifth after Denard Span exchanged words with Lee. Span was upset that Lee threw an inside fastball as he called time-out. After he grounded out, Span stopped between the plate and the mound on his way back to the dugout and said something to Lee. Players ran on the field, but nothing happened.
"He kept looking at me so I just said, `If you're going to stand there in the box, be ready to hit,'" Lee said. "I'll take that strike every time, but I threw a ball."
Lee allowed two runs -- one earned -- and four hits, striking out five in seven innings.
Strasburg was hurt by an error on right fielder Jayson Werth, who dropped a foul ball two pitches before Marlon Byrd hit a three-run homer in the first inning. The hard-throwing right-hander gave up three unearned runs and six hits, striking out five in six innings.
"After the first inning, I had better command on my fastball," Strasburg said.
Jerry Blevins (2-0) retired the two batters he faced in the seventh to earn the win. Rafael Soriano tossed a scoreless ninth for his sixth save in six tries and extended his scoreless streak to 23 innings, dating to last season.
The Phillies, who played just their second game in five days, have lost two in a row at home after a 6-4 trip to the West Coast. They had two scheduled off days this week and another game was rained out.
Strasburg retired the first two hitters before Chase Utley and Ryan Howard hit consecutive singles. Werth then let Byrd's fly ball bounce off his glove after a long run near the foul line. One pitch later, Byrd lined a 96 mph fastball into the seats in right-center to give the Phillies a 3-0 lead.
Lee left with a 3-2 lead, but the NL's worst bullpen promptly blew it.
Span led off the eighth with a double off Adams. He stole third and scored on Anthony Rendon's single to center to tie it at 3-3. Werth followed with a single up the middle. Diekman replaced Adams and allowed LaRoche's go-ahead RBI hit to center.
"They just keep battling," Nationals manager Matt Williams said. "Coming back is a trait they have. They fight. It's a very good sign."
Ian Desmond followed LaRoche's single with a double to right that just eluded Byrd's diving attempt. Diekman escaped further trouble by striking out Danny Espinosa and Moore with runners on second and third. After Jose Lobaton walked to load the bases, Diekman struck out pinch hitter Zach Walters.
Tyler Moore connected off Lee in the third to cut it to 3-1.
Moore started the fifth with a single, advanced to third when Lobaton reached on second baseman Utley's fielding error. After Strasburg sacrificed, Span drove in Moore on a groundout to Utley.
"It seems like we have a quiet confidence," Moore said.
The Phillies' relievers have a 5.07 ERA and have blown six saves, though closer Jonathan Papelbon is 8-for-9.
"We've been good in the eighth and ninth innings to this point, so it's disappointing," Phillies manager Ryne Sandberg said.
Moore is 6-for-12 with two homers off Lee. ... Lee had four walks entering the game, but walked two, including Strasburg on four pitches. ... Former Phillies closer Brad Lidge, who was 48-for-48 in save chances during Philadelphia's 2008 World Series championship season, will throw out the first pitch Saturday night. ... RHP Tanner Roark (2-0, 2.76) goes for the Nationals against Philadelphia's A.J. Burnett (1-1, 2.15) on Saturday night.
31,945 (73.2% full) - % is based on regular season capacity
68 degrees, partly cloudy
Home Plate - Jim Reynolds, First Base - Manny Gonzalez, Second Base - Sean Barber, Third Base - Fieldin Culbreth
Stephen Strasburg (WSH) allowed 3 unearned runs in the first inning, thanks to a Jayson Werth error with 2 outs...
He's allowed 16 unearned runs since the start of last season, 2nd-most in the majors (Wily Peralta - 23)
Cliff Lee walked Stephen Strasburg on 4 pitches in the 3rd inning.
It's only the 4th time in his career Lee has walked the pitcher but the first time he's done it on 4 pitches.
The Nationals are hitting .259 against curveballs from lefties in 2014, which is 26 points better than the league average. Cliff Lee has surrendered a .273 batting average in at-bats that he has ended with a curveball this year.