The pair ended at 23-under-par 193, one stroke better than two other teams at the Westin Savannah Harbor Resort and Spa.
The title was Faxon's second on the Champions Tour and Sluman's fourth.
The combination of Gene Sauers and Kenny Perry fired the low round of the day -- 10-under 62 -- to end in a second-place tie at minus-22.
Jay Don Blake and Roger Chapman, who held the lead after 36 holes, tumbled to a 1-under 71 Sunday, ending in a 16th-place tie.
Notable deaths of 2014 [PHOTOS]