Steve Nash paced Phoenix, scoring 22 points and dishing out 16 assists. Grant Hill posted 18 points and Channing Frye dropped 13 and pulled down 11 rebounds for the Suns, who have lost three straight and four of five.
Phoenix lead throughout most of the game, but saw their lead dwindle to just four, 77-73, at the end of the third period.
"The game was really decided in the second half and we really played up to our ability," Smith said. "We played like we're supposed to be playing throughout the whole game."
Atlanta kept pushing early in the fourth, and after Nash was called for a technical foul with the game tied at 81, Smith knocked down a free throw to give the Hawks their first lead since a 13-12 edge early in the first quarter.
The Hawks built off that momentum, turning a bad pass and two missed shots into six more points to cap off a 12-0 run, giving them an 88-81 lead just under the midpoint of the final stanza.
Atlanta would build a lead as large as nine before Phoenix began charging. Down 98-92, Nash drove into the paint, sunk a layup and was fouled with 42.9 seconds to play. His free throw made it a three-point game.
After missed jumpers on both ends of the floor, the Suns fouled Smith with 9.5 seconds to play. Smith made one of two, Phoenix called a timeout, and Nash was fouled as he went up for a shot under the post. He swished both, and the Suns were down just two.
After the requisite foul, Green made both free throws to make it a four-point Hawks edge once more. Nash missed a three-pointer on the next trip down the floor, but Frye was there for the putback dunk. With only 2.1 seconds left on the clock, however, Phoenix was unable to foul in time, and Atlanta escaped with the win.
"It sounds like it's Groundhog Day all over again," said Suns guard Jared Dudley, who scored 11 points. "We had a lead, a double-digit lead, and they came back. It's happened a little too often. We're having these dry spells of scoring."
Hill scored nine of his points in the first quarter and the Suns held the Hawks to 39.1 percent shooting from the floor in the first quarter to hold a 31-21 advantage after one. Phoenix enjoyed a 56-47 lead at the half.
Smith's 30 points tied a season-high. Green's 20 set one...Phoenix reserve Markieff Morris fouled out with 9.5 seconds remaining...The Suns concluded their first back-to-back-to-back since the 1998-99 season...The Hawks are 13-0 when shooting 45 percent or better from the field. They shot 47.5 percent Wednesday.