Denver led by 13 early in the fourth quarter, but Minnesota cut its deficit to two on a 3-pointer from Kevin Love with 19 seconds remaining.
Wilson Chandler was then fouled and he made his first free throw to give Denver a three-point cushion. Chandler missed his second try, but Miller came dashing in from behind the 3-point line to snare the rebound.
That forced Minnesota to again foul and Miller made 1-of-2 from the line to seal the win.
Chandler had 19 points and Kenneth Faried added 16 points and 10 rebounds. It was Denver's third straight win.
Love led Minnesota with 28 points and 10 rebounds.
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