The former U.S. Open champion birdied three of the last nine holes for a four-under-par 67 and an 11-under total of 202 at the Innisbrook Resort.
"I'm just happy with the round," American Furyk told reporters after covering the back nine in three-under 32.
"I felt like I played real solid on the front nine, missed a couple good birdie putts.
"But I got on a little bit of a run on the back nine and it turned out to be a good score."
The 2003 U.S. Open champion has not triumphed on the U.S. circuit since the 2007 Canadian Open, a barren run of 58 events.
"I've had quite a few opportunities to win," Furyk said. "Sometimes I've hit poor shots or I've played poorly, shot a bad round and got myself out of it.
"When you're playing poorly or you don't play well, it's easy to lose your confidence and it takes a lot longer to build it up.
"But I've also had a lot of events ... where I really felt good about my game and walked off the course knowing that I gave it my all, and really played my rear end off, but just got beat.
"I want to go out and win a golf tournament," added the 13-times PGA Tour winner.
"That's what we play golf for. That's what I practice hard for, and I haven't been able to do that in over two-and-a-half years."
(Editing by Greg Stutchbury)