Harden led the way with 21 points in what was Houston's second straight win. Boston, which embarked on a three-game road trip, had won two in a row.
The Celtics were within five inside the 5-minute mark, but Harden hit a 3-pointer that began a 13-6 surge that finished off the contest.
Boston overcame a sluggish start to take a two-point halftime lead, but Houston took the lead for good just 1:02 into the third period.
Paul Pierce scored 18 points for the Celtics. Rajon Rondo pitched in 15 points and 13 assists.
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