The Nationals, who have the worst record in the majors at 58-103, sent the Braves to their fifth loss in a row.
After both teams scored two runs in the 10th, Pete Orr singled with one out in the Nationals 11th and moved up on a sacrifice. Maxwell followed with his fourth homer, a drive over the right-field fence against Manny Acosta (1-1).
Zack Segovia (1-0) earned his first win despite giving up two runs in the 10th. Atlanta tied it at 4 on an RBI double by pinch-hitter Kelly Johnson and run-scoring single by pinch-hitter Greg Norton.
Logan Kensing got his first save of the season with a scoreless
Pinch-hitter Christian Guzman hit a two-out, two-run double in the 10th that put Washington ahead 4-2 lead.
The Braves had won 15 of 17 to get within two games of Colorado in the wild-card chase on Monday before the latest losing streak.
Atlanta reliever Peter Moylan got the first two outs in the 10th before Ryan Zimmerman doubled. Adam Dunn was intentionally walked before Guzman doubled over the head of right fielder Omar Infante.
The Nationals had taken a 2-0 lead on a first-inning RBI single by Zimmerman and a solo home run by rookie Ian Desmond in the fourth off Jair Jurrjens.
The Braves tied it at 2 on a two-out, two-run single by Brian McCann off Ron Villone in the sixth.
Jurrjens went eight innings, gave up five hits and struck out nine. Washington starter Ross Detwiler went five innings and allowed one hit, a bunt single to Nate McLouth leading off the game.
NOTES: Atlanta OF Matt Diaz's season ended when he had a cyst removed from his infected right thumb after Friday night's game.... Washington OF Willie Harris left the game in the fifth inning with a strained right oblique. ... The Nationals are 4-0 when Desmond homers. ... Jurrjens has allowed 2 or fewer earned runs in 26 of his 34 starts.