First prize was worth $1 million.
"I think the first thing is I can't believe it was this long since the last (win)," Cink said.
"I feel like I've played well enough along the way to have won a couple, but sometimes when you have to wait a little bit you have to go through a few extra trials and it seems a little bit sweeter."
Mahan and Armour both shot 65 in the final round, ending at 17-under-par 263.
Heath Slocum (67) was fourth at 16-under 264 and Vijay Singh (68) fifth, another two shots back.
The round was interrupted by a one-hour rain delay.
"I had the lead all weekend and we had to endure a rain delay and guys were firing left and right," Cink said.. "And I just stayed a step ahead, just enough ... ."
Celebrity Families of 2014 [PHOTOS]