The Suns' lead was at 95-89 after Kyle Korver hit his fifth 3-pointer at the 3:54 mark, and down to 95-91 on a basket by Mack with 3:22 to play.
Mack made it a one-point game with a layup to cap an 8-0 run, but the Suns scored seven of the last eight points of the third quarter to take a 102-95 lead into the fourth.
Leandro Barbosa, playing his first game since missing the past five with a sprained toe, scored five key points in the fourth quarter to keep the Hawks at bay. The Suns never held less than a five-point lead in the quarter.
A transition pass from Dragic to P.J. Tucker for a long jumper made the score 121-110 with 3:20 left in the game and essentially ended any chance for a Hawks comeback.
"They shot the ball extremely well. They play with great pace, they put lot of pressure in your defense, make or miss," Hawks coach Mike Budenholzer said. "Our transition defense wasn't good enough."
The Hawks have lost 11 of their last 12 games. The Suns haven't lost two straight games to the Hawks since the 1991-92 season.
It took Korver less than two minutes to continue his NBA-record streak of at least one made 3-pointer in a game. His long-range shot at 10:29 of the first quarter gave him 127 straight games with a made three-ball.
Korver made six of seven 3-pointers to finish with 18 points.
NOTES: Newly acquired power forward Shavlik Randolph made his Suns debut Sunday. He played 10 minutes and scored two points off the bench. ... Hornacek said guard Eric Bledsoe, who is coming back from knee surgery earlier this season, looked good in 5-on-5 action in practice recently. Bledsoe hasn't played since Dec. 30. The Suns want Bledsoe's conditioning to return to game level before allowing him to play, which could keep him out for another two weeks. ... Budenholzer is a native of Holbrook, Ariz., in northeastern Arizona, and had family and friends at Sunday's game. ... Hawks F Paul Millsap missed his fourth straight game with a right knee contusion. ... C Mike Muscala, signed late last week, made his Hawks debut and played 19 minutes. He had four points, five rebounds and two blocked shots.