The trio charged to the top of a congested leaderboard to finish the day level at six-under par at the tricky Copperhead layout at Innisbrook Resort.
But the tournament remains wide open with another 13 players, including defending champion Luke Donald, lurking within three shots of the leaders.
Streelman shot a flawless round of six-under 65 to grab the early clubhouse lead as PGA Tour rookie Shawn Stefani quickly fell away.
Stefani, who led by a shot overnight, bogeyed four of his first eight holes before salvaging a three-over-par 74 to end the day just two off the pace.
Leonard got to seven-under but dropped a shot with a bogey on the 15th hole while South African Coetzee birdied the 17th to join Streelman in a three-way share of the lead.
"I wanted to get to six-under today," Streelman said.
"I had that number in my mind to at least have a chance going into tomorrow so I was happy to get there."
Jim Furyk birdied the last hole to join his fellow Americans Ben Kohles and Tag Ridings and Australia's Greg Chalmers at minus five.
Donald was among five players who finished at four-under while another four players, including Spain's Sergio Garcia, were a shot back but still right in contention at three-under.
After struggling for consistency on the first two days, Donald, who won last year's Tampa Bay Championship in a four-way playoff, carded a bogey-free round of four-under-par 67 to move into a tie for ninth place.
"It was nice to go around this course and not make a mistake," the Englishman said.
"It could have been a really low round today. But I'm certainly moving in the right direction...I feel like my game has been close, and obviously starting to show with some results."
- Sports & Recreation
- Luke Donald