Korver was 3 for 6 behind the arc as the Hawks built a 52-44 halftime lead.
Alonzo Gee's 3-pointer drew the Cavs within 58-56 with 8:16 left in the third quarter.
"(The Cavs) were playing real carefree," Smith said.
But Cleveland would never be that close again even as Speights scored 12 straight points for the visitors in the fourth quarter.
Notes: Al Horford returned to start at center for Atlanta after missing two games with a stomach illness. He had 16 points and six rebounds before fouling out in the fourth quarter. . . . The only players with longer 3-ball streaks than Korver and Miller were Dana Barros (89), Michael Adams (79) and Dennis Scott (78). . . . Cavs guard Daniel Gibson was ejected with 7:07 left in the second quarter after drawing a pair of technical fouls. The first came for griping too passionately at official Brent Barnaky when he didn't get a foul call against Atlanta as he missed a shot. Then, Gibson and Atlanta's DeShawn Stevenson drew technicals in an ensuing debate about the situation. . . . . Cleveland's C.J. Miles missed the game with a sore right ankle. . . . Tristan Thompson returned to action for the Cavs despite suffering a laceration above his left eye that require three stitches.