Washington entered the game needing a win and a loss by the New York Knicks on Sunday to make the playoffs. The Wizards are sixth in the Eastern Conference.
Wall scored 13 points in the last 7:16 of the third quarter and the Wizards finally escaped the pesky Hawks, who have lost six straight and 20 of 26.
Washington led 99-89 with 2:38 to play, but the Hawks scored eight straight including three free throws by Lou Williams and a three-point play by Teague with 39.8 to play. Teague's three points came immediately after Wall missed two foul shots.
With the Wizards leading 99-97, Marcin Gortat blocked Teague's shot with 11.1 seconds left. Gooden was fouled by Teague and hit two free throws to secure the win.
Washington followed up a 13-point win over Eastern Conference leader Indiana on Friday with a win over the Hawks, who lead the Knicks by 1 games for the final playoff berth in the East.
The Wizards' postseason position wasn't an issue for coach Randy Wittman.
"If we play the way we're capable of playing, we don't have to worry about any of those things," Wittman said.
Atlanta coach Mike Budenholzer, whose team played well despite missing three of its five leading scorers, had a similar mindset.
"I think every game our group has shown flashes and been good," Budenholzer said. "When we play with really good energy and we compete, you can see where we can have the results we're looking for."
The Hawks started hot, hitting seven of their first eight shots and running off to a 21-11 advantage, but Washington got eight late points from Gooden, outscoring the Hawks 16-7 in the last 4:31 to lead 28-27 after one.
Thanks to nine points in the last five minutes by Pero Antic, Atlanta led 52-50 at halftime.
Wall's third-quarter offensive display gave the Wizards a 75-71 lead after going into the fourth.
Washington F/C Nene, who has missed 17 games with a left knee sprain is progressing, though Wittman isn't guessing when he may return. "He's going on the floor a little bit, on his own, just kind of getting on his legs a little bit," Wittman said. "Where that takes us I don't know. He's going in a good direction.". Atlanta was without G/F Kyle Korver (back spasms) and G DeMarre Carroll (stomach virus).. Wizards G Andre Miller was called for a flagrant foul on Hawks G Dennis Schroder in the fourth quarter, but Schroder missed both foul shots.