It was the second victory in two exhibition games for the Hawks, who also defeated Orlando on Monday.
Williams and Smith got lots of offensive support. Ex-Sun Joe Johnson scored 14 points, Flip Murray had 13 and Al Horford and Acie Law 10 each.
Shaquille O'Neal topped the Suns with 21 points and 10 rebounds in 23 minutes. Alando Tucker scored 14, Matt Barnes and Louis Amundson 12 apiece, and Grant Hill 10.
The Suns, playing without Amare Stoudemire (torn iris in right eye) and Leandro Barbosa (personal reasons), showed off their newfound defensive prowess in the first quarter. They held the Hawks to 12 points -- only two in the final six minutes -- on 29.4 percent shooting (5-for-17). During the period, they also limited Atlanta's reserves to two shots and no points in a total of 19 minutes.
With the subs on the floor for most of the second quarter, the pace picked up and so did the scoring. At halftime, Phoenix led 44-37 as reserve Tucker led the way with 10 points and newcomer Amundson had nine. Starters Williams and Johnson each scored nine for Atlanta. Overall, the Suns' second team outscored Atlanta's No. 2 unit 24-3.
Surprisingly, the Suns, one of the league's most prolific 3-point shooting teams in the league last season, failed to hit from long range, missing all three of their attempts, and they had only four fastbreak points, another sharp contrast to a year ago, when they frequently pushed the ball up court under Mike D'Antoni.
Phoenix quickly broke its 3-point drought in the second half, making their first two, one each by Steve Nash and Raja Bell. But with the starters playing most of the minutes in the third period, the Hawks solved the Suns' defense, outscoring Phoenix 36-26 for a 73-70 lead by the end of the quarter. Smith was the catalyst, scoring 10 points, while Zaza Pachulia added eight.
They hung on in the fourth period, building a 91-83 lead on a basket by Williams -- who also had two 3-pointers in the quarter.
The Suns will be playing three exhibition games in four days, most unusual for the preseason. On Thursday night they will be at Utah, and Saturday they will face Denver at Indian Wells, Calif., in the NBA's first outdoor game in the modern era. ... The Hawks and Suns will meet again Oct. 15 at Atlanta. ... Atlanta guard Speedy Claxton sat out Wednesday night with a pulled hamstring.