"It's life in the NBA," Spoelstra said of the constant shuffle. "Everybody has to deal with that. So at least we've had some experience with it so far this season."
The Rockets also were short-handed, without reserve guard Eric Gordon and starting forwards Ryan Anderson and Trevor Ariza. That had forwards Luc Mbah a Moute and P.J. Tucker in Houston's starting lineup, along with Clint Capela, Harden and Paul.
As with the teams' previous game this season, the Heat found themselves positioned for the upset, this time up 87-85 early in the fourth quarter, before Houston scored the next nine points.
From there, Richardson matched his career high in points and 3-pointers with a 3-pointer to draw the Heat within 94-90, only to see his 3-pointer matched by one from Paul.
But with Harden converting a 3-pointer with 2:50 to play, Houston was able to push to a 104-94 lead. Another Harden 3-pointer, with 2:03 to play, made it 107-94, effectively ending it.
The Heat briefly moved into the lead in the third quarter before going into the fourth down 83-80, with Paul scoring the Rockets' final seven points of the third.
Harden was up to 28 points by then, with Dragic with 24 and Richardson with 22.
The Rockets entered 33-2 this season when carrying a lead into the fourth.
With Dragic scoring 10 consecutive points at one stage late in the second period and closing the quarter with 13, the Heat trimmed what had been a 17-point deficit in the period to a 61-57 halftime deficit.
Harden was up to 23 points by the intermission, with Dragic with 20 at that stage.