Douglas guarded Robinson after that, and Robinson only scored two points the rest of the way.
"I felt like Toney gave us our best chance to win," Houston interim coach Kelvin Sampson said. "He was a better matchup with Nate."
The Bulls' offense bogged down at the end, and Douglas' 3-pointer with 1:11 remaining put Houston up 86-84. The Rockets acquired Douglas in a trade that sent Marcus Camby to New York in July.
"He works so hard," Harden said of Douglas. "He had the courage to step into that shot and shoot it."
The Bulls got two offensive rebounds, but Robinson flipped a wild pass from under the basket that hit Deng's hands and went out of bounds.
Douglas sank two free throws and former Bulls center Omer Asik blocked Noah on a drive.
Chicago has lost three in a row for the first time since a 10-game slide between Feb. 27 and March 19, 2010. The Bulls held a team under 100 points for the first time in five games, but couldn't get the stops when they absolutely needed them.
"Our defense is not what it used to be," Noah said. "It's not what it was last year, that's for sure. We have to do better. Losing three in a row is unacceptable. We're better than that."
The Bulls led the league in scoring defense last season (88.2 points per game), and Thibodeau is seeing inconsistency this year.
"The big thing on defense is everyone has responsibility," he said. "We have to stay disciplined and we have to stay attached and we can't make things up. The fourth quarter is different. Your intensity is higher and you have to stay disciplined."
Notes: Chandler Parsons had 18 points and a career-high 13 rebounds for Houston. ... Harden tied a career high with five steals. ... The Rockets have won the last two meetings with Chicago after losing the previous five. ... Boozer has three double-doubles in his last four games.