Cousins was able to shake off the early foul trouble and took over late in the fourth quarter to lift the Kings to a 110-106 victory over the Rockets on Tuesday night.
Rudy Gay had 25 points to help in the victory.
On the next play, Cousin took a charge from Harden to give the Kings the ball back.
"DeMarcus has proven and shown many times that he's willing to give up his body in key situations," Sacramento coach Michael Malone said. "To see him do that, to be in the right spot to give his body up and give us an extra possession is big-time. He had a great game."
Cousins admitted that he gets a little too excited to face marquee players like Dwight Howard.
"I was so antsy, I was so pumped to play well," he said. "I guess you could say that got me in foul trouble."
The late comeback ruined a big night by Harden, who finished with a season-high 38 points and had 10 rebounds and two steals.
"The first half we were sluggish we didn't play with any energy," Harden said. "The second half we played a lot harder (but) we can't keep coming up short and coming out with these slow first halves."
Gay has scored at least 20 points in seven of his 10 games since being traded from Toronto. Cousins had 17 points, 16 rebounds and four steals, and Marcus Thornton added 15 points.
Isaiah Thomas scored six straight points for Sacramento to give the Kings a 101-100 lead with 2:39 remaining. That spurt was capped by his only 3-pointer to extend his streak of 24 straight games with at least one 3-pointer, which is the fourth-longest streak in team history. He had 17 points and 10 assists.
A dunk by Terrence Jones and a jump shot by Harden put Houston back up 104-101 before Cousins went to work.
Howard had 15 points and eight rebounds for Houston, and Jeremy Lin added 14 points and six assists.
"We shouldn't have let them stick around," Howard said. "We allowed that to happen and they played with confidence in the second half, they hit shots and they got a good win."
Houston coach Kevin McHale can't figure out why his team struggles to play consistently.
"We've played some poor games and this was another," he said. "It doesn't feel like we're in much of a rhythm."
The game was tied when Harden took over, scoring six of the points in an 8-1 run to give Houston a 98-92 lead with 5 minutes left. He capped it with a 3-pointer with rookie McLemore right in his face and held up three fingers on each hand as the crowd went wild.
Cousins made a dunk which he was fouled on to cut Houston's lead to 88-84 with about 9 minutes remaining. He slipped after the dunk and remained face down on the court laughing for a few seconds before getting to his feet and missing the free throw.
His dunk was part of a 10-2 run that tied it at 90 with 7 minutes left.
Quincy Acy gave Sacramento a one-point lead with a layup with about 3 minutes left in the third quarter. The Rockets regained the lead with a 10-3 run to end the quarter and make it 86-80.
Sacramento had a 60-52 lead early in the third quarter before Harden got hot. He scored nine points for Houston during a 15-7 spurt that put the Rockets up 67-65.
Jason Thompson received a technical after that for a clear path violation when he pushed Harden in the back on a fast break. Harden finished the play after the whistle with a one-handed dunk before making one of two free throws.
Houston C Omer Asik missed his 15th straight game with thigh and knee injuries. ... Sacramento has scored at least 100 points in its last seven games. ... All of Houston's starters have scored in double figures in the last two home games.