Power carded his third straight six under 65 - while Griffin signed for a 66 - around Port Royal Golf Course, enough to take the pair to 18 under for the tournament, two shots ahead of Aaron Baddeley and Kevin Yu.
The Irishman enjoyed a bright start on Saturday, rolling in four birdies in his first five holes and made the turn at five under. A double-bogey on the par three 13th slowed Power's momentum, but he bounced back with a brave birdie on the treacherous par three 16th before sinking another on the 17th.
"I knew I had to get birdies before 11," Power told pagatour.com.
"I was able to hang in there and it puts me in a good spot going to tomorrow."
The daunting 16th tee shot was made even more gnarly on Saturday. The ocean lines the entirety of the left hand side of the hole and the wind was ripping from left to right...
"I don't know how comfortable you get when you get to 16 and you're having to aim your ball in the ocean," quipped Power, who found the green and rolled in a 30-footer for birdie.
Meanwhile, Griffin - who actually gave up golf citing the financial pressure it put on his parents - had just one blemish among six birdies on his card.
"You don't ever know what the world is going to bring you," said the American of his financial backers that helped him rejoin golf in 2021.
"You just need to be thankful for all the people who are there to help you."