Simpson played a bogey-free round, ending at 18-under-par 262, three better than George McNeill (6-under 64).
Tommy Gainey grabbed sole possession of third place at minus-14 with a 1-under 69. Charles Howell III (67), Jerry Kelly (65), Vijay Singh (65), 2008 champion Carl Pettersson (69) and Kyung-tae Kim (66) all shared fourth at minus-13.
Padraig Harrington, meanwhile, cracked the Top 125 on the FedExCup points list with a 47th-place finish Sunday.
Ernie Els and William McGirt also qualified and will be taking part when the playoff begin at Barclays next week.
Missing the FedExCup cut, however, were Matt Jones, David Mathis and Cameron Beckman.
Celebrity Breakups and divorces of 2014 [PHOTOS]