It was the Clippers' first win in Salt Lake City since 2003, snapping a string of 16 consecutive losses - including a 108-79 loss in Utah on Jan. 17.
Paul sat out that the last visit with a left hamstring injury. He had 12 points in the fourth quarter in this game as the Clippers won their fourth straight.
Al Jefferson had 27 points and 12 rebounds to lead the Jazz.
The Clippers made eight free throws in the final 30 seconds.
Utah's C.J. Miles intentionally missed his second free throw with the Jazz down two points with 1.2 seconds left but Reggie Evans grabbed the rebound to seal the win.
Paul, Griffin lead Clippers past Jazz, 107-105
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