TAMPA, Florida, March 14, 2013 (AFP) - The 31-year-old American is coming off a season-best tie for 39th at the Puerto Rico Open last week.
"I wasn't really starting the day with a lot expectations," said Stefani after notching six birdies, noting that he just wanted "to go out and have fun and hit some good shots."
Brian Harman posted a bogey on his final hole and is alone in second at four-under 67 on the Copperhead Course at Innisbrook Resort and Golf Club.
Harris English shot a three-under 68 and is tied in third with two other Americans, Tag Ridings and Brendan Steele. English had been on course for second spot on the leaderboard before a double bogey on his last hole.
Two-time champion K.J. Choi, of South Korea, and Fiji's 2004 winner Vijay Singh both carded two-under 69s.
They are in a group of eight alongside Australian Geoff Ogilvy, Peter Tomasulo, Dicky Pride, Lucas Glover, Chez Reavie and Roberto Castro.
Stefani began his round on the back nine and started quickly with back to back birdies. On the opening hole he managed to stick his second shot inside two feet. He made it two birdies in a row at No. 11 by chipping his third shot to four feet.
He missed the green at the par-five 14th but chipped to two feet to post his third birdie. Stefani tacked on three more birdies on the first five holes of the front nine before parring his final four holes.
Harman, who also started on the back nine, charged up the leaderboard with three-straight birdies beginning at the par-five fifth.
"I stayed real patient today," Harman said. "Never pushed when I really wanted to.
"I drove it well and stayed in play. When I hit it out of play, I just hit it up there in front and tried to make par."
Defending champ Luke Donald, whose victory last year propelled him to top spot in the world rankings, stumbled home with three bogeys on the last four holes to finish at one-under 70.
"I am extremely disappointed," said England's Donald, who was four-under through his first 14 holes. "I had it really under control and could have been six or seven under with a couple of putts.
"Obviously to finish like that, it leaves a bitter taste in my mouth."
Donald and Choi were accompanied by 2010 winner Jim Furyk who shot a one-over 72.
Donald beat Furyk, South Korea's Bae Sang-moon and Robert Garrigus in a four-man playoff last year.
Donald is one of seven players ranked in the world top 20 in the field this week. He is also one of eight former champions participating, including South Africa's Retief Goosen, who won in 2003 and four years ago.
Goosen shot a disappointing five-over 76 on Thursday.
Leading scores on Thursday after the first round of the $5.5 million Tampa Bay Championship (USA unless noted, par 71)
65 - Shawn Stefani
67 - Brian Harman
68 - Tag Ridings, Brendan Steele, Harris English
69 - Chez Reavie, Vijay Singh (FIJ), K.J. Choi (KOR), Dicky Pride, Peter Tomasulo, Roberto Castro, Lucas Glover, Geoff Ogilvy (AUS)
70 - JJ Henry, Luke Donald (ENG), Nick Watney, Patrick Cantlay, Billy Horschel, Marc Leishman (AUS), Scott Brown, Adam Scott (AUS), Jason Day (AUS), Jerry Kelly, Trevor Immelman (RSA), Justin Hicks