Al Horford had 21 points and 10 rebounds and Jeff Teague scored 20 points to help the Hawks win for just the second time in their last 10 road games.
With the Hawks up 99-98, Harris poked the ball from a driving O.J. Mayo and saved the ball from going out of bounds with 23.9 seconds left.
Dirk Nowitzki scored 24 points and Mayo added 19 for the Mavericks, who have lost two of the first three on a five-game homestand.
Dallas, which didn't lead until the fourth quarter, pulled ahead 91-86 on five straight points from reserve Brandan Wright. Smith responded with a dunk and 3-pointer to tie the score midway through the fourth.
Smith whipped a pass to Horford for a dunk that stretched Atlanta's lead to 96-92 and he hit a 3-pointer over Nowitzki that made it 99-94 with 1:29 left.
Nowitzki connected on a pair of free throws and short shot over Smith that cut it to 99-98 with 44.9 seconds remaining.
Smith lost the ball to Elton Brand and Mavericks got the ball in transition to Mayo, who was driving for the go-ahead basket. Harris, who was drafted by Dallas in 2004, sneaked up from behind and tipped the ball from Mayo. He saved the ball to Smith and the Hawks hit all six of their free throws in the final 22.2 seconds to preserve the victory.
Harris scored 15 points for Atlanta, which has gone 8-12 since starting the season 20-10.
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Darren Collison scored 14 points and Vince Carter chipped in with 13 for the Mavericks.
The Hawks led by 13 in the first half before the Mavericks rallied to pull to 49-48 at halftime.
Collison's 3-point play tied the score at 64 midway through the third.
Kyle Korver hit a 3-pointer in transition and John Jenkins followed with a basket to give Atlanta an 82-74 advantage.
The Mavericks scored seven points over the final 1:04 of the third, capped by two free throws from Nowitzki, to pull to 82-81.
NOTES: Atlanta coach Larry Drew said Smith hasn't paid much attention to hearing his name in trade rumors as the Feb. 21 deadline approaches. "He's been able to keep his focus and be professional about it," Drew said. ... The Mavericks have scored 100 points in 13 of their last 15 games. ... Korver has hit a 3-pointer in 44 straight games, the longest active streak in the NBA.
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