Once Mayo shifted the dribble to his right hand, Harris knew he had a chance to knock the ball loose and help the Atlanta Hawks pick up a rare road victory.
Atlanta was up 99-98 when Elton Brand knocked the ball away from Smith. Mayo picked it up and was driving for the go-ahead basket.
Harris, who played 3½ seasons with the Mavericks before he was sent away as part of the Jason Kidd trade in 2008, snuck up from behind and poked the ball away from Mayo. He then saved the ball from going out of bounds with 23.9 seconds left.
"I just kind of wanted to sit behind and see if he would put the ball back in his right hand," Harris said. "When he did, I was able to steal it away at the right time."
Smith connected on two free throws to extend Atlanta's lead to 101-98. Needing a 3-pointer to tie it, Mayo made a bad pass that the Hawks stole with 14.9 seconds remaining.
"Obviously, we're disappointed," Mayo said. "It was a winnable game. We didn't make the plays down the end and they made some plays."
Al Horford had 21 points and 10 rebounds and Teague added 20 points and nine assists.
The Hawks came into the game having lost eight of nine road games since Jan. 4.
"Any time you go on the road and get a win, it's always big," Atlanta coach Larry Drew said. "We've had our ups and downs, as most teams do. But we have not fragmented when that has happened."
Even though the game was decided late, coach Rick Carlisle was disappointed in Dallas' rough first quarter. The Mavericks fell behind 10-0 and trailed by as much as 13 early.
"I didn't have our guys ready to play," Carlisle said. "You've got a team of guys that just goes out and is walking around at the beginning of a game. That's on the coach."
Dallas, which didn't lead until the fourth quarter, took a 91-86 lead when Brandan Wright scored five straight points. Smith answered with a dunk and a 3-pointer to tie the game at 91 with 5:44 left.
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.
That set up the frantic final seconds where the Hawks held on for their eighth win in 20 games after starting 20-10.
Smith was 10 of 15 shooting, including four 3-pointers, and handed out six assists. The forward knows his name has been in trade rumors that have surfaced in the past few days.
"I'm just trying to focus on getting better as an individual on the court," Smith said. "As long as I'm with the Atlanta Hawks, I can only focus on how to make this team better."
Dallas rebounded from its slow start to pull within 49-48 at half.
Darren Collison's 3-point play tied the score at 64 midway through the third.
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.
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. ... Harris started for the first time since Jan. 30 and finished with 15 points and five assists.