Horford was largely responsible for Cousins' mediocre game. The Kings center was limited to 11 points and six rebounds.
Cousins made his first three shots in the game's opening minutes, but didn't score again until getting a three-point play at the 11:21 mark of the fourth quarter. He was then called for three quick fouls early in the fourth, and he went to the bench for good at the midway point of the period.
''My teammates did a great job of disrupting him and were digging real well and keeping him off balance,'' Horford said. ''Any given night he can be the best big man in the league. Mentally, I feel he's stronger this season.''
When asked about Horford, Cousins' only reply was, ''Next question.''
Horford received plenty of help from Millsap, a key offseason addition for the Hawks. The two combine to give the Hawks a strong inside presence. That was evident in the fourth quarter when Horford scored 10 points and Millsap had eight, combining for 18 of Atlanta's 23 points.
''Paul has a knack for scoring late [in the game],'' Atlanta coach Mike Budenholzer said. ''I think both Paul and Al stepped up for us. They are working well off each other.''
The Hawks (2-2) led by 17 points going into the fourth quarter, but the Kings cut it to three with 32 seconds left. Isaiah Thomas had a chance to tie it with three seconds left but missed a 3-pointer and the Hawks beat the Kings for the 11th straight time, including six straight in Sacramento.
Atlanta shared the ball effectively throughout and were getting open looks for much of the game until the final six minutes. The Hawks shot 48 percent, made eight 3-pointers, and had only six turnovers going into the fourth quarter when they committed eight more in helping to fuel the Kings' comeback.
''The defense isn't where it should be obviously right now, and we continue to dig ourselves in big holes,'' Kings coach Mike Malone said. ''Every time you do that you have to fight out of it and that takes a lot when you're 19 points down.''
Jeff Teague, who left the game in the first quarter with an ankle problem, returned in the second and played well, finishing with 18 points and 10 assists for Atlanta. Both Kyle Korver and Cartier Martin had nine apiece.
Thomas has made a habit of coming off the bench this season and providing the energy that has the Kings in up-tempo mode on offense and hustling defensively. However, there was no helping the Kings in the second and third quarters when they were outscored 57-33.
''We just can't keep doing this to ourselves like we are some great team,'' Thomas said. ''It takes a toll on your whole team. We keep coming back, but it's not going to happen every night.''
Using a suddenly energized defense in the fourth, the Kings scored 11 straight points, cutting the Hawks lead to 96-95 at the 2:45 mark on a fast-break layup by Thomas.
When the lead had been reduced to three points at the 3:04 mark, Millsap brought the Hawks together for a little inspirational talk.
''It was one of those moments when everything was unraveling,'' said Millsap, who played the previous seven seasons with Utah. ''I told everyone, `Let's finish this game.' That's my personality, to lead.''
Millsap was inspirational with his play as well. With the clock running down and Atlanta's lead reduced to one point, he made an 8-footer and added a free throw for a 99-95 lead.
After dominating the second quarter, the Hawks controlled the third. Getting numerous open looks against the Kings' lackluster defense, Atlanta went on a 19-6 run for a 75-56 lead at the 4:47 mark.
Korver connected on his first 3-point attempt early in third quarter, extending his streak to 77 straight games, the fourth longest in NBA history and one less than third place Dennis Scott. Dana Barros holds the NBA record with 89.
Teague scored 14 points and Millsap had 13 in the opening half. The Hawks trailed the entire half until the midway point of the second quarter. They ended up outscoring the Kings 29-13 in the second to take a 54-45 lead into halftime.
McLemore had 12 first-half points for the Kings, who had 12 turnovers. The Kings are in the midst of a seven-game stretch in which they play six home games. Their only away game is Friday at Portland.
The two teams play again Saturday night in Sacramento.
Boxing champion Floyd Mayweather was sitting in a courtside seat. ... Kings rookie point guard Ray McCallum dressed for the first time this season, replacing center Hamady Ndiaye on the active roster. ... Salmons had seven points in the first quarter and the Kings shot 12 of 22 in leading 32-25. ... Atlanta concludes a three-game road trip Thursday night in Denver.