In Thursday's opening round, both players shot 9-under 63.
"I heard coming up here how good the (Hamilton Golf & Country Club) course was and I think it definitely met expectations," said Furyk, who is playing this tournament for the first time since 1999. "It's a very good one."
The score by Furyk and Rose bettered the former course record 8-under 64, set by Tommy Armour in 1930.
"I feel like I'm playing a little better," said Rose, who tied for fourth place at last week's Deutsche Bank Championship.
Brandt Jobe, Frank Lickliter II and Nathan Green are tied for third at 6-under 64.
Sean O'Hair and four others are tied for sixth at 5-under 65.
Defending champion Mark Calcavecchia is tied for 11th place at 4-under 66.
Swim Week Miami Beach 2014 [PHOTOS]