All four homers -- Morse hit No. 26 in the sixth inning -- came against Hiroki Kuroda (11-15), who entered with a career-high four-game winning streak. The right-hander had a season-high nine strikeouts, but gave up five runs and eight hits in six innings.
Lannan (9-11), who had lost his previous four starts, allowed one run and five hits in 5 1/3 innings. Collin Balester, Tom Gorzelanny, Tyler Clippard and Sean Burnett combined for the final 3 2/3 innings.
Morse drove in three runs and was one of five Nationals with two hits. The first baseman-outfielder leads the team in home runs, average (.315) and RBIs (82).
"Over the course of my career I've hit behind some pretty good hitters. Mike is having a big year," said Werth, who often followed Ryan Howard and Chase Utley in Philadelphia's lineup before signing with the Nationals last winter.
"When I signed here he was one of the guys I really liked and thought he had a chance to be a really good player. He's really done a good job this year and turned himself into a force to be reckoned with and a guy going forward who's going to be a pillar in this organization."
Kuroda had never allowed three or more home runs in the same game, let alone the same inning. The four-year veteran threw 114 pitches.
"Usually, when you don't pitch good, it's that first inning," Los Angeles manager Don Mattingly said. "(Kuroda) got himself into a groove and pitched well after that. He gave us some chances to kind of creep back in."
Lack of run support was a factor in Lannan's skid as the Nationals scored a combined five runs in that stretch. They nearly generated that output in the first inning against Los Angeles.
"They kind of had the momentum right there in the first inning," said Desmond, who has two leadoff home runs in the last three games. "It was nice for us to answer back and then continue to keep it going the rest of the game. That's something we haven't done this year."
After Rick Ankiel singled and Ryan Zimmerman's fly ball was caught at the wall, Morse's drive cleared the fence in left. Werth followed with another shot to left, also on a slider, for the fourth set of back-to-back home runs by the Nationals this season.
"I didn't have my slider in the first inning, or throughout the game," Kuroda said through an interpreter.
"I felt pretty good. A little hiccup there in the first, but I settled down after they scored," said Lannan, who threw 27 of his 94 pitches in the first inning. "It's always a little bit of a comfort when you can go out there and just try and get ahead knowing that you have a lead."
Justin Sellers hit an RBI double in the ninth for Los Angeles.
Ankiel doubled in Desmond in the seventh, and Wilson Ramos had an RBI single in the eighth.
The Dodgers entered having won four consecutive series. ... Rain is forecast throughout the day on Tuesday, potentially interfering with Stephen Strasburg's season debut. The No. 1 overall pick in the 2009 draft is returning to the majors after undergoing Tommy John surgery last fall. "If (Strasburg) warms up and it rains, we'll probably have to do it another day," Washington manager Davey Johnson said. ... Johnson acknowledged a wave of minor leaguers are expected to be called up on Tuesday. Eastern League Pitcher of the Year Brad Peacock and second baseman Stephen Lombardozzi are the expected headliners.
The Philadelphia Phillies are reportedly one of the teams showing interest in free-agent lefty reliever Jake McGee.
Baltimore is reportedly looking at free-agent right-hander Lance Lynn as it looks to shore up its starting rotation.
Brandon Kintzler finished the season as a setup man for the Nationals, but he is drawing plenty of interest as a closer in the free-agent marketplace.
The timing might not be right to get a big return for its star closer, but Baltimore could be left with no choice but to trade him this winter.
Atlanta Braves prospect Ronald Acuna won the Arizona Fall League MVP award after finishing with seven home runs in 23 games for the Peoria Javelinas.
As Toronto looks to add a left-hander to upgrade its bullpen, the Jays are reportedly interested in former Red Sox reliever Robbie Ross Jr.