When they learned they'd be without coach Kevin McHale against Detroit, they were even more determined to break the losing streak.
Harden scored 20 points, Omer Asik had 14 and the Rockets beat the winless Pistons 96-82 in their first game without McHale.
The team announced earlier Saturday that McHale was taking an immediate leave of absence to deal with a family matter.
Assistant coach Kelvin Sampson took over, and said before the game that he hoped the team would come together to win for McHale.
The Rockets did just that, using a third-quarter run to build a big lead and go on to their first victory at home. The Pistons fell to 0-7.
"It was good for us to come out here and get a win, especially for coach McHale and what he's going through," Harden said.
Jeremy Lin said it was a bit strange to play without McHale in charge of the team.
"It was definitely different," Lin said. "He's our leader. He's our voice. But coach Sampson did a good job coming in, and we played hard. Obviously we can't wait for coach McHale to come back. Everybody around here loves him to death."
Brandon Knight scored 16 points for Detroit and Greg Monroe added 12 points and 11 rebounds.
Detroit scored five quick points to get within four midway through the third quarter. The Rockets responded with an 11-2 spurt highlighted
Harden was fouled on a layup he made after a nifty assist from Lin during that run. Harden slapped the padded part of the goal after the shot, and promptly knocked down the free throw for the three-point play.
Sampson, who was a longtime college coach before moving to the NBA, acknowledged that it felt odd to be working as a head coach again for the first time since 2008.
"I was nervous at first," he said. "I kept tonight in perspective. I kept thinking of Kevin and his family and what he's going through. That's something far more important than me coaching a game for the first time in (almost) five years."
Houston padded its lead by scoring the first eight points of the fourth quarter. Detroit couldn't do anything offensively in the fourth quarter and missed its first 10 shots.
The Pistons didn't score in the quarter until Knight's jump shot with six minutes remaining made it 80-59.
"There was no offensive energy out there at all," Detroit coach Lawrence Frank said. "We didn't even give ourselves a chance during that run. I don't make excuses why because I know we're capable of doing more."
Detroit's Tayshaun Prince, who scored 13 points, was unhappy with the team's performance.
"The way we are playing right now is unacceptable," he said. "Guys should be upset right now."
Houston came in averaging almost 20 turnovers a game but had a season-low 14 against Detroit.
This was the second meeting between these teams this season. Harden scored 37 points and had 12 assists in a 105-96 victory in his debut with the Rockets on Oct. 31 after a trade from Oklahoma City days earlier.
Marcus Morris added 12 points for Houston and Toney Douglas had 11. Lin helped out with seven points, eight assists and four rebounds.
Houston was up 72-57 entering the fourth quarter.
The Rockets were up by five at the end of the first quarter, and used a 14-7 run capped by a 3-pointer from Douglas to open the second quarter and extend the lead to 34-22.
Houston's lead was 15 points late in the second quarter before Detroit scored nine straight points to end the period and cut the Rockets' lead to 47-41 at halftime.
NOTES: Houston rookies Terrence Jones and Donatas Motiejunas made their NBA debuts on Saturday night. Jones had five points and two blocks and Motiejunas had three points . ... Houston's Chandler Parsons has made at least one 3-pointer in each game this season. ... There is no timetable for McHale's return.