The Nationals, meanwhile, can't seem to score much by any means -- or win the close games they dominated earlier this season.
Jeff Kent hit one of four homers that accounted for all of Los Angeles' runs in a 5-4 victory over slumping Washington, which has lost its last 11 one-run games.
Jason Phillips, Jason Repko and pinch-hitter Hee-Seop Choi also connected, the first time this season a visiting club hit more than two homers at Washington.
"That's a lot of home runs hit in this ballpark. That's kind of strange," Nationals second baseman Jose Vidro said. "One run short. It is frustrating every time now. We're looking like we're down the stretch now. We can't afford to keep losing. We've got to find a way."
Entering the night, a total of 52 home runs had been hit in 50 games at RFK Stadium, which hadn't been used for a regular-season Major League Baseball game since the Senators left after the 1971 season.
During batting practice, several Dodgers noticed that the best way to hit homers at RFK is to the gaps and down the lines, where each of Tuesday's four shots traveled.
"We kept them out of the middle of the field," Phillips said. "The middle of the field is big."
Several Washington players felt vindicated last month when the team remeasured and determined that the outfield gaps were more than 10 feet farther from home plate than originally marked. But the Nationals have trouble scoring everywhere lately, with or without power.
In their last 15 games -- of which they've lost 12 -- never have they scored more than four runs. On Tuesday, Washington went 1-for-10 with runners in scoring position and left eight on base. Seven of its nine hits were singles.
"It always seems to come back and get us at the end when we don't take advantage of those opportunities early in the game," said outfielder Brad Wilkerson, who was stranded after hitting a two-run triple with one out in the third inning off winner Jeff Weaver (9-8). "We've been doing that a lot lately."
Before the recent drought in one-run games, the Nationals surged to the top of the NL East thanks to a 24-8 mark in such contests. Now they're 5½ games behind Atlanta in the division and trail Houston in the wild-card standings.
"When you're winning those games, it has a positive effect on you," Nationals manager Frank Robinson said. "When you're losing those games, it has a negative effect."
The Dodgers, meanwhile, had lost two in a row and four of five to fall 11 games under .500 entering Tuesday.
Weaver left after facing one batter in the seventh inning. He allowed two runs and six hits. Yhency Brazoban pitched the ninth for his 21st save. After Vidro nearly was thrown out legging out a double with two outs, Brazoban retired Jose Guillen on a grounder to end it.
Nationals starter Esteban Loaiza (6-7) gave up three homers, including Kent's shot on the first pitch of the second inning. That gave Kent 20 homers for the ninth consecutive season -- a record for a second baseman.
"The final trip he makes will be to Cooperstown," Dodgers manager Jim Tracy said.
Repko hit his sixth homer of the season in the fifth, and Phillips broke a 2-all tie in the seventh with a two-run shot after Kent doubled.
Choi made it 5-2 in the eighth with his first career pinch-hit homer. It came on reliever Hector Carrasco's second pitch of the night.
The Nationals scored on Vinny Castilla's sacrifice fly in the eighth off reliever Steve Schmoll. Then, with runners at the corners and Jonathan Broxton pitching with two outs, the Nationals pulled to 5-4 thanks to an unearned run. Preston Wilson stole second, and Dodgers catcher Dioner Navarro's throw sailed into center field for an error that allowed Guillen to trot home from third.
Broxton walked Brian Schneider, then forced pinch-hitter Carlos Baerga to ground out to end the inning.
The Dodgers' four homers tied their season high. ... The Nationals are the only team in major-league history to win 12 consecutive one-run games and lose 11 such games in a row in the same season.