The Rockets passed the Boston Celtics for the longest winning streak in the NBA this season.
Trailing by about 10 points for most of the fourth quarter, Milwaukee got within 104-99 with 1:06 left on Sterling Brown's layup.
Chris Paul answered with a short floater in the lane with 45 seconds left after driving on Jason Terry to silence Bucks fans who were pleading "Defense!
Houston obliged after forcing the Bucks to waste 15 seconds on the ensuing inbounds pass and settle for an off-balance 3 that missed.
Houston got off to a sloppy start at the Bradley Center with a seven-turnover first quarter, a night after tying its season high with 22 turnovers in the 10-point win at Oklahoma City.
Harden hit a deep 3 just before the halftime buzzer from well beyond the arc with a defender in his face for a 58-46 lead.
Rockets: Swingman Joe Johnson missed a second straight game due to illness, while coach Mike D'Antoni rested Nene a day after the center played 17 minutes.
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