The Trail Blazers trailed by nine points with 2 1/2 minutes remaining but Damian Lillard's 3-pointer and Hickson's slam dunk ignited a 10-0 run to finish the game.
Hickson (15 points, seven rebounds) was fouled by Blake Griffin with 45 seconds left and sank the decisive throws, while the Clippers' Jamal Crawford missed a pair of shots in the closing seconds to seal the Trail Blazers' win -- their second straight following a six-game skid.
Nicolas Batum had 20 points, 12 assists and 10 rebounds and Lillard finished with 20 points for Portland.
Griffin struck for 24 points, 10 assists, eight rebounds and four steals for Los Angeles, which dropped its fourth straight.
Celebrity Families of 2014 [PHOTOS]