Fredi Gonzalez is sticking with Craig Kimbrel — even after the rookie closer blew his third save.
Alex Cora drove in two runs with a bases-loaded single in the ninth as Kimbrel gave up a 3-1 lead.
"It's a cruel game, it really is," said Gonzalez, in his first season as Atlanta's manager. "We just couldn't get those last three outs. You just hope the learning curve is there and I think it is. We'll keep running him out there."
Drew Storen (3-1) pitched the 10th and Tyler Clippard took over in the 11th for his first save.
The Nationals improved to 5-1 in extra-innings games. The Braves are 1-4 in extra innings.
Desmond drove in both runners with his double down the third-base line. Werth followed with his sixth homer to add to the lead.
Brian McCann's two-run double in the first inning gave Atlanta the lead it held until the ninth.
Laynce Nix, who had three hits, and Jerry Hairston Jr. had ninth-inning singles before Kimbrel loaded the bases in the ninth with a one-out walk to pinch-hitter Matt Stairs. Cora followed with two-run single past Kimbrel to tie the game.
It was the third blown save in 10 chances for Kimbrel, who gave up three hits and a walk in the inning.
"Everybody went out there and played good, the entire team did," Kimbrel said. "And I didn't go out there and do my job. I'm leaving balls over the plate. It's just bad execution by me."
The Braves have turned to Kimbrel as the team's new closer following Billy Wagner's retirement. Kimbrel, a hard-throwing right-hander, has a 2.70 ERA.
Hinske said he tried to encourage Kimbrel following the loss.
"That's part of baseball. You can't save every game," Hinske said. "I just told him afterward, 'Hey, don't lose our confidence. Don't lose your swagger. We've got your back. You're going to have to do it again tomorrow.'"
Added Hinske: "This is a tough loss, there's no way around that."
The burly Hinske came through with a surprise defensive highlight in the fifth when he raced to the gap in right-center to catch a long flyball hit by Roger Bernadina. With the Braves leading 2-1, Hinske hit his fourth homer off Doug Slaten in the seventh.
Tommy Hanson gave up five hits and one run in 5 2-3 innings.
With runners on second and third, Kimbrel struck out Desmond and Werth to end the inning.
Heyward's MRI could lead to more opportunities in right field for Hinske, who also has started in left field and at first base this season.
Heyward said Wednesday he has had soreness in the shoulder since spring training. He said the situation became more of a problem Tuesday night when his right hand went numb and he couldn't shake it off, forcing him to leave the game in the eighth inning.
John Lannan couldn't extend his streak of wins in three straight starts against the Braves, including a home win on April 2. Lannan threw five straight scoreless innings after allowing two runs in the first.
Lannan gave up five hits and two runs in six innings. He walked three and struck out three.
McCann, who hit another double in the eighth, has an 11-game hitting streak.
The Nationals scored a run off Hanson in the second. Wilson Ramos doubled and scored on a single by Nix.
Notes: Hairston was thrown out by McCann while trying to steal third base to end the seventh. ... RHP Peter Moylan will have surgery next week to repair a bulging disk in his lower back. Moylan said the operation, tentatively planned for Tuesday in Los Angeles, won't end his season. He said he has been told the recovery could take eight to 12 weeks. ... SS Alex Gonzalez started after missing one game with a sore left hamstring. ... Jones' double in the 11th was the 505th of his career, breaking a tie with Roberto Alomar for third all-time for switch-hitters.