"I was open and my teammates were finding me," he said. "I struggled early in the season, but I've been in a good rhythm lately and my shot is starting to feel right."
Jason Thompson had 19 points and 10 rebounds for the Kings. Marcus Thornton had 17 points, Tyreke Evans finished with 14 and Aaron Brooks scored 13.
Cousins returned after he was suspended the previous two games for a verbal altercation with San Antonio TV analyst Sean Elliott. Cousins, who was whistled for a technical foul in the third quarter, had nine points, 16 rebounds and seven assists, but missed 11 of 15 shots.
"He was rusty, he has been out of rhythm for two games," Kings coach Keith Smart said. "Sometimes you come back and you're probably being hard on yourself, trying to get out of a slump. We're having a very rough time and it's not fun for anyone."
Ahead by 12 points, Smith had a dunk, Horford hit two free throws, and Ivan Johnson scored from close range, increasing the lead to 98-80 with 7:55 left in the fourth.
The Hawks squandered a big second-quarter lead, but came out strong in the third, outscoring Sacramento 28-14.
Korver played a key role in a 9-0 run in the third. He began the spurt with a 3-pointer and finished it off with a long jumper, putting the Hawks ahead 81-69 with just over three minutes left in the period.
Sparked by their second unit, the Kings got going with a season-best 36-point second quarter. Brooks was the catalyst, making three 3-pointers and scoring 13 points in helping cut the margin from 18 early in the period to 58-56 by halftime.
NOTES: Evans, who entered the game 1 of 11 on 3-pointers, hit his first attempt in the opening quarter. ... Drew was a starting guard for the first Sacramento Kings team that relocated from Kansas City for the 1985-86 season. ... Kings small forward James Johnson was wearing glasses for the first time this season. The glasses didn't help the poor-shooting Johnson, who was 1 for 7 from the field. ... In a shooting slump the previous five games, the Hawks shot 58 percent in the first quarter and led 34-20 after one.