The 2003 US Open champion started the day one behind overnight leader Arjun Atwal, but birdies on the second, third and sixth holes lifted him to the top of the leaderboard on 12 under.
India's Atwal was among a trio of players sat behind Furyk on 10 under. He had carded a bogey and a birdie after seven holes.
Atwal is currently 175th on the PGA Tour money list and needs a high finish this week to move into the top 125 and secure his card for 2013.
Bud Cauley began his third round with a bogey but then picked up shots on the second, fourth and seventh to sit alongside Atwal through eight holes.
United States captain Davis Love III was also in that group having completed seven holes of his third round and mixing two birdies with a bogey.
Peter Tomasulo was making his move up the standings and sat on nine under after 11 holes, with birdies on the fifth, eighth and 11th holes.
A group of eight players, including three-time major winner Vijay Singh, were tied on eight under midway through the third round.