The American holed five birdies to move to eight under, while Canada's Graham DeLaet had an eagle and three birdies in a 68 to reach seven under.
Ryan Moore (69) and fellow American Charley Hoffman (67) are at five under.
World number one Jordan Spieth improved to two under after a four-under 67, while England's Danny Willett (71) is the best of the Britons on level par.
"On this golf course, the leaders start getting four-to-five footers on greens that are a little inconsistent, who knows what's going to happen," said defending champion Spieth.
"I really like the position we're in. Obviously the lead would be better but we've got momentum on our side."
Haas, the son of nine-time PGA Tour winner Jay Haas, has twice finished in the top 10 this year but is in contention for his first win of 2016.
He paid tribute to the influence of his father, who joined him at Innisbrook earlier in the week.
"He came up with the swing thought I've had for three days, and I'm leading," said Haas. "Without him coming down, I might not even have made the weekend. It was very valuable.
"If it goes south, I can blame him."
Bill Haas hit a four-under 67 to take a one-shot lead into Sunday's final round of the Valspar Championship in Florida.