After the Suns pulled to 95-94 on Miles Plumlee's short jumper with 38.8 seconds left, Lou Amundson scored on a dunk 5 seconds later to give Los Angeles a 97-94 lead and Kendall Marshall missed a jumper on Phoenix's ensuing possession.
Clippers coach Doc Rivers spent the second half in the Clippers' locker room with an undisclosed illness. Los Angeles assistant coach Alvin Gentry, who was fired by the Suns on Jan. 18, took over the sideline duties.
Playing its presumptive starting lineup for the first time, Phoenix cut into the Clippers' lead at the start of the second half.
Gortat and Dragic scored six points each, and Eric Bledsoe hit a 19-foot jumper with 4:16 left in the third quarter to pull the Suns within 66-63.
But Paul scored on consecutive jumpers and set up Jordan for a thunderous alley-oop dunk over Bledsoe as Los Angeles pushed its lead back to 76-66 to end the third.
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Six teams now have meetings scheduled with premier free-agent target Kevin Durant, a league source confirmed to ESPN.