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.
Houston continues to struggle on the road with a 10-17 record. The Rockets play road games against Golden State and the Clippers before the All-Star break.
"It's definitely a setback and I feel like we gave this one away," Chandler Parsons said. "On the road, coming down the stretch we have to take it. It's only going to get harder on this road trip with Golden State and in L.A.. Those games now are a lot bigger."
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.
"When we're playing well this place is rocking," Hayes said. "I've been an opponent on the other team and it gave me goose bumps. This place can get really loud. Fans here have been unbelievable. They are passionate."
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. The Rockets were 10 of 33 overall. ... These were the Kings only back-to-back home games of the season.