The American recovered from a couple of early bogeys to finish on two-under for the day, nine-under for the tournament.
Some excellent shots on the back nine particularly at 12 and 17 have put Furyk in an excellent position.
Overnight leader Jason Dufner is one shot back, recovering from a double-bogey at five to finish with eight consecutive pars in tough conditions.
Henrik Stenson carded a round of 69 to finish one further back on seven-under for the tournament.
The 37-year-old will play alongside his compatriot Jonas Blixt, looking to become the first Swedish player to win a Major.
A double-bogey on 16 ruined what was looking like a good round of level par for Adam Scott, although after two hard-fought pars to finish, the Australian will still fancy his chances tomorrow from five-under.