The Rockets were coasting at 102-89 with seven minutes and 50 seconds remaining when Harden dunked the ball with such ferocity it went through the net and back onto the rim.
Officials mistakenly judged the dunk had not passed fully through the hoop and the decision ultimately proved costly as the Rockets blew their comfortable lead in a match in which Harden scored 50 points at the AT&T Center.
Crew chief James Capers later conceded the field goal should have counted but said the Rockets missed their window of opportunity to call for a review on the play.
"When the play happened, Harden goes in for a dunk, and then the ball appears to us to pop back through the net," Capers told reporters.
"When that happens, that is basket interference. To have a successful field goal, it must clear the net.
"We have since come in here and looked at the play. He dunked it so hard that the net carried it back over the rim a second time, so in fact it did clear the net and should have been a successful field goal.
"The play could have been reviewed, it is a reviewable matter, but you have a window of 30 seconds to challenge the play during that timeout that he had and while they were protesting the call, trying to get clarification of it, that window passed.
"So therefore, it elapsed and they were not able to do it."
Speaking prior to Capers' comments, Rockets coach Mike D'Antoni offered a different version of events.
"I have no idea [why it didn't count]," he said. "I heard that they said the ball hit James and went back through, so it was a goaltend on James.
"I challenged that, and I didn't get a response. Then another guy said it wasn't a goaltend; it went out of bounds on us.
"And I said, 'Well, I challenge that.' Can't do that. I don't know, [how] to answer your question. I've got nothing. I can't tell you."
Asked about the incident, Harden merely replied postgame "it went in" while team-mate Russell Westbrook offered a succinct summation.
"S*** happens. Plain and simple," he said.
ESPN reports suggest the Rockets are hopeful of either being awarded the win or having the final minutes replayed at a later date.