The Kings were trailing by 10 points early in the fourth quarter, but Thomas led an offense that was difficult for the Rockets to match in the fourth quarter.
Houston was outscored 17-7 over a four-minute stretch when the Kings took control of the game.
Kings center DeMarcus Cousins had 20 points despite sitting out much of the second half with foul trouble. Jason Thompson scored 12 points, and Francisco Garcia came off the bench and had 11, including six points in the fourth quarter when the Kings outscored Houston 33-25.
James Harden had 30 points, six rebounds and four assists for Houston, which lost for the fourth time in five games. Patrick Patterson scored 18 points and Omer Asik had 17 points and 12 rebounds. Carlos Delfino added 15 points and Jeremy Lin finished with 12 points and six assists.
The Rockets pulled within a basket, but Salmons, who had 10 fourth-quarter points, was quickly fouled and made both free throws for a 115-111 lead with nine seconds remaining.
A late jumper by Harden was off the mark, and the Kings secured the rebound.
Fouled on a 3-point attempt by Harden, Salmons converted all three free throws to put the Kings up 111-107. Fouled with 25 seconds left, Thomas made a pair of free throws for a 113-107 lead.
The Kings converted 26 of 27 free throws in winning their second straight game.
Thomas made a 3 and later converted on a three-point play with 5:07 left, tying the game at 100. Thomas hit another 3-pointer a short time later, then drew the sixth foul on Lin. Thomas made both free throws to give Sacramento a three-point lead with 2:40 left.
Ahead by two points and with Harden resting on the bench, the Rockets opened the fourth quarter with eight straight points, the final two on a driving layup by Patrick Beverly that put them in front 94-84.
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Sacramento was coming off a high-energy, emotional win Saturday against Utah. A boisterous crowd cheered the Kings from start to finish when chants of keeping the team in Sacramento were prevalent throughout.
The crowd of 15,526 wasn't nearly as vocal on Sunday, but they were on their feet several times. A organized fan-based effort is urging people to demonstrate support for the team and bolster attendance for the remainder of the season.
The Kings are 3-8 since the announcement Jan. 21 that the Maloofs had agreed to sell a controlling interest of the Kings to Chris Hansen's Seattle-based ownership group.
That group intends to move the Kings to Seattle if the sale is approved by the NBA. Sacramento Mayor Kevin Johnson is leading the effort to find new owners and keep the Kings from relocating.
Harden scored 10 points in a fast-paced third quarter when Houston shot 65 percent and outscored the Kings 33-27. Delfino converted on a corner 3 to end the quarter, giving the Rockets an 86-84 lead heading into the fourth.
After scoring six points early in the period and hitting the 20-point plateau, Cousins picked up his fourth foul midway through the third quarter and went to the bench. He re-entered the game early in the fourth and quickly got his fifth foul and left the game.
Cousins came out shooting from the perimeter early and found success. He scored 10 of his 14 points in the first quarter and helped the Kings take a 57-53 lead into halftime. Harden scored 15 points for the Rockets.
NOTES: Evans picked up two fouls in the game's first six minutes while guarding Harden. ... Earlier in the day, Rockets reserve center Greg Smith was sent to the Rio Grande Valley Vipers. Smith is in his second season and averaged 5.5 points and four rebounds in 44 games. ... Houston, which is on pace to break the franchise record for most 3s made in a season (705), was 6 of 16 in the first half. ... This was the Kings only back-to-back home games of the season.
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