Korver made seven consecutive 3-point attempts on his way to a season-high 28 points, leading the Hawks to a 124-107 victory on Wednesday.
"Those are dangerous games," Korver said. "We kind of said when the fourth quarter started that we've got to pick it up right now."
Al Horford added 25 points and 10 rebounds for the Hawks, who have won two straight and five of seven. Jeff Teague finished with 18 points and tied a career high with 15 assists.
DeMarcus Cousins scored 28 points, Rudy Gay had 22 and Isaiah Thomas 20 for the Kings, who allowed a season high in points.
The Hawks outscored the Kings 39-20 in the fourth quarter of their 12th consecutive victory against Sacramento. Horford made back-to-back jumpers to help Atlanta open a 117-105 lead with 2:49 left.
"I guess I'm not doing a good enough job of giving them a game plan that they can execute," Sacramento coach Michael Malone said, "and I'm not doing a good enough job of explaining who the players are on their team that can make shots."
Korver missed his first 3 attempt early in the first, but then hit seven in a row before missing midway through the fourth. He went 8 for 10 from long range while extending his NBA record to 95 consecutive games with at least one 3-pointer.
Korver finished with his highest point total since Nov. 21, 2007, when he scored 31 for Philadelphia in a 104-84 home victory against New York.
"I got a lot of really good looks tonight," Korver said. "I usually don't get that many. That was a product of a lot of our spacing and just everyone knocking down shots."
Atlanta finished with 38 assists for its highest total since it had 39 in a 136-104 home victory against Philadelphia on April 19, 1997.
"That's the product of a lot of things," Korver said. "It's unselfishness, it's good spacing, it's a lot of guys in rhythm, it's everyone being dangerous and no one's really sure where the help is going to come from [on defense]. When Jeff is attacking like that and really going to the basket, it really creates a lot of openings for us."
There were 14 lead changes in the third quarter. Late in the period, Gay stole the ball from Teague and drove the length of the court for a reverse layup that put the Kings up 78-75, but Teague answered with a 3 on Atlanta's next possession.
Sacramento grabbed the lead for the first time early in the second quarter. Jimmer Fredette had a jumper and a 3-pointer, and Cousins' tip-in made it 33-30 with 9:38 to go.
The Hawks had a quick response. Korver made his third 3 and Mike Scott's alley-oop dunk put Atlanta ahead by six about 3 minutes later.
"It was a back and forth game," Teague said. "Everybody was scoring. We couldn't stop each other. Luckily we got some stops in the fourth."
Gay, who was playing with right knee stiffness from Tuesday's loss at Charlotte, hit a jumper in the final minute of the second to put Sacramento up by one.
Scott hit consecutive 3s from the left corner early in the fourth, his second one making it 93-91 and giving Atlanta the lead for good.
After resting to begin the fourth, Cousins returned with 7:44 remaining, but he was nearly shut down offensively, hitting his only field-goal attempt after being very active in the paint throughout the first three quarters.
Led by Korver, the Hawks went 15 for 25 from 3-point range.
"When you play against guys like that, like known shooters, you've got to play with more urgency," Cousins said. "That's something we didn't do tonight and the results of that, he had an incredible game."
Kings minority owner Shaquille O'Neal was at the game. ... DeMarre Carroll scored 15 points and Paul Millsap had 14 for Atlanta. ... Korver's 3-point streak began in his second game with Atlanta on Nov. 4, 2012, in a victory at Oklahoma City. ... Sacramento's previous high in points allowed this season was 122 in a home loss to Utah last Wednesday. ... Atlanta had the game's biggest lead at 14 when Millsap hit a 3 late in the first. ... The Hawks were without F Cartier Martin (sprained left ankle) and C Gustavo Ayon (sprained left ankle, bruised left leg). ... Kings F Carl Landry missed his 14th straight game with a torn hip flexor.