The Nets went on a 36-13 run after the Kings scored 10 straight points to tie the game in the third quarter. They have won a season high-tying seven games in a row at home and 14 of their last 16 at Barclays Center.
Thornton came to the Nets on Feb 19 in a trade that sent Jason Terry and Reggie Evans to Sacramento.
"It's always fun to play your former team and see your homeboys," said Thornton, "but my job was to focus on getting this win and we did."
Joe Johnson scored 18 points and Deron Williams and Shaun Livingston each had 10 for Brooklyn, which has won five of six overall.
The Nets were without Kevin Garnett for the fifth straight game because of back spasms and lost two more players to injury.
Paul Pierce left the game just 73 seconds into the first quarter with what the team said was a sore right shoulder and Andrei Kirilenko went out in the third with a sprained right ankle.
DeMarcus Cousins had 28 points and 20 rebounds to lead Sacramento and Rudy Gay scored 20. The Kings are 1-2 on a seven-game road trip and have dropped five of their last seven overall.
They beat the Nets 107-86 at home on Nov. 13 and were trying to sweep the season series between the teams for the first time since 2007-08. The Nets swept the two-game set last season.
The Kings, down by as many as 16 in the first half, rallied to tie the score with a 10-0 run in the third quarter led by Gay's five points.
But Jason Collins scored at the other end to give Brooklyn the lead for good. The Nets stretched their advantage to 12 by the end of the quarter thanks to a Thornton 3-pointer in the final seconds and went up by 23 just over three minutes into the fourth.
Earlier, Pierce was guarding Jason Thompson down low when the Kings big man made a spin move toward the basket and made contact with Pierce's shoulder.
He made his only shot, a layup to start Brooklyn's 17-4 run to open the game. Six Nets players scored during the run, punctuated by Johnson's give-and-go alley-oop pass to Livingston for a dunk.
Brooklyn carried a 28-19 lead into the second quarter and went up by as many as 16 points three times before taking a 49-40 advantage into halftime.
"I don't think we were ready to play tonight," said Kings coach Mike Malone. "We were able to cut it to nine at halftime, which was a gift because it wasn't a nine-point game if you watch that half."