Stefani, who for the first time earned his way onto the PGA Tour this year at the age of 31, shot a 1-under 70 at the Innisbrook Resort for a two-day total of 7-under 135. In his six previous starts during his rookie season he has missed the cut three times and finished no better than a tie for 39th.
After firing a 65 on Thursday, Stefani made his first two bogeys of the tournament but held things together over one of the more difficult courses on the tour.
"I hope to just keep doing what I've been doing," Stefani said.
Tied for fourth place at 137 were Jason Dufner, Peter Tomasulo, Harris English and Brian Harman.
The day's low round of 65 was turned in by two-time heart transplant recipient Erik Compton, who finished in a tie for 13th at 140.
Defending champion Luke Donald settled for a 72 and an even-par total of 142.
It took a score of 144 to survive the 36-hole cut and among those missing it was John Daly, who needed 10 shots to play the par-4 third hole and eventually shot an 81 for a 153 total.