The Rockets and Kings were playing each other for the second time in three days following Sacramento's 121-118 win on Wednesday.
"I thought everybody contributed, and when we needed a stop or a basket, different guys did it for us," Kings coach Alvin Gentry said. "We had guys stepping up, and I think that's the main thing. It was a really good team win."
For Sacramento, Damian Jones had 17 points, 17 rebounds and six blocks, Donte DiVincenzo had 19, and Chimezie Metu had 18. Barnes made 10 of 16 from the field, including 4 of 6 from 3-point range.
"We just want to play good basketball, finish these games out and see where it goes," Jones said. "We all played our part and fought to the end."
Houston rookie Jalen Green scored a career-high 33 points and had six 3-pointers. He was coming off a 32-point night on Wednesday and topped 20 points for a fifth straight game.
"I feel like I draw a lot of attention," Green said. "When you attack the middle, a lot of people are going to close in so I just have to be there for my teammates and get to the rim."
Kevin Porter Jr. had 27 points and 11 assists for the Rockets, and Garrison Mathews had 22 points on 6 of 10 shooting from 3.
The Kings finished the third quarter trailing 91-86, but opened the fourth on an 8-0 run to take a 94-91 lead. Sacramento outscored Houston 36-26 in the fourth quarter.
"We had a bunch of good looks, a bunch of good shots that just didn't go," Rockets coach Stephen Silas said. "The fight that our group is showing is great. I just wish we could come up with the results."
Hot first-quarter shooting helped the Rockets to a 41-26 lead early and they led by as much as 19 points in the first half, but Sacramento came back to tie the game late in the second quarter.
Houston led 62-57 at halftime.
Tempers flared from the sideline throughout the game. Gentry received a technical just 1:14 into the game after yelling at the officials and Silas received a technical later in the third quarter following a foul call.
The game was interrupted midway through the third quarter by a streaker, who stripped down to his underwear and danced midcourt for a few seconds before being taken down to the floor and carried out by security.
"That was pretty funny," Jones said. "It looked like it hurt, to be honest, being tackled by them dudes."
SILAS ON FRUSTRATIONS
"For these guys to be going through these moments, it's big for our group. In the fourth quarter, those were big minutes. It does get frustrating at times, but I can't be frustrated with this group and how they're playing. It's frustrating that we lost, but these guys are playing," Silas said.
Former Rocket Robert Horry sat courtside for the game. Horry, who won two of his seven championships with the Rockets, attempted - and drained - the pregame First Shot free throw for charity.
Kings: Sacramento was without De'Aaron Fox (right hand soreness), Domantas Sabonis (left knee contusion) and Richuan Holmes (personal). ... The Kings made 12 of 28 3-pointers for 42.9%.
Rockets: Rookie C Alperen Sengun missed the game with a left leg contusion. Dennis Schroder (left shoulder soreness) missed a third straight game. ... Usman Garuba had a career-high 14 rebounds.
Kings: Host Minnesota on Sunday.
Rockets: Host Golden State on Sunday.
Kevin Porter Jr. puts Chimezie Metu on skates
Kevin Porter Jr. hits the bucket after an absolute dime of a move on the Kings' Chimezie Metu.