Atlanta has won four in a row and is 3-0 on a six-game road trip. Utah has lost back-to-back home games for the first time since late December.
Horford had 34 points and 15 rebounds while Smith pitched in with 24 points and 14 boards. Atlanta built a 15-point lead with 7:30 to play.
Al Jefferson scored 26 points and had 11 rebounds for Utah. Derrick Favors added 17 points and a season-best 15 boards.