James Harden (C) of the Houston Rockets drives past Justin Hamilton (L) and James Ennis of the Miami Heat during their NBA game at American Airlines Arena in Miami, Florida, on November 4, 2014James Harden (C) of the Houston Rockets drives past Justin Hamilton (L) and James Ennis of the Miami Heat during their NBA game at American Airlines Arena in Miami, Florida, on November 4, 2014 (AFP Photo/Mike Ehrmann)
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Harden was just one rebound shy of a triple-double, scoring 25 points with 10 assists and nine rebounds for the Rockets, who also got 26 points from Dwight Howard.
With the win the Rockets are off to their first 5-0 start since opening 6-0 during the 1996-97 season.
They'll face another formidable test when they host the reigning champion San Antonio Spurs on Thursday.
"We always want the test," Harden said. "Our next game against San Antonio in Houston is going to be a test as well. We're going to approach every game the same way -- both ends of the floor make sure we're together."
Chris Bosh, wooed by the Rockets as a free agent in the off-season before re-signing with the Heat -- staying put despite the departure of superstar LeBron James after four seasons in Miami -- had 21 points and eight rebounds for Miami, who opened the season with three straight wins.
Dwyane Wade added 19 points but it wasn't enough to get the Heat off to their first 4-0 start since they won five straight to start the 2011-12 campaign.
The Rockets shot 51.5 percent from the floor and hit 17 of 37 from three-point range.
Harden was a perfect 10-of-10 from the free-throw line, improving to 61-of-64 from the foul line this season.