Molinari, who shot a bogey-free round, is at 13-under.
Woods finished the day with a round of 67. He had issues early but recovered with three straight birdies on holes six through eight.
Finau finished the day at 64 and will be remembered for being just the fifth golfer in history to shoot a 30 on the front nine.
In the final round Sunday, players will begin to tee off in threesomes starting at 7:30 a.m. because of the threat of severe weather moving, tournament officials announced. The leaders will tee off at 9:20 a.m.
Molinari, Woods and Finau will comprise the final group.
Brooks Koepka shot a 69 to fall to fourth place behind Woods and Finau, shooting a 4-under that sits him at 10 under for the tournament.