Streelman was joined by Justin Leonard (67) and George Coetzee (68) atop the leaderboard at 6-under-par 207 after 54 holes on the Copperhead Course at Innisbrook Resort and Golf Club.
"It was one of those days I played smart and made putts when I needed to," said Streelman. "I wanted to get to 6-under today. I thought that was a good number to at least give me a shot tomorrow."
Jim Furyk also moved his way up the leaderboard with a 4-under 67 to nab a share of fourth place. He was joined by Ben Kohles (69), Greg Chalmers (69) and Tag Ridings (70) a shot back of the leaders at 5-under.
Kohles and Chalmers were among the players tied at the top of the leaderboard entering their final holes, but recorded bogeys to fall a shot off the pace.
Shawn Stefani, who was the leader at the conclusion of both the first and second rounds, struggled to five bogeys and just two birdies en route to a 3- over 74, falling into a group of five players tied for eighth place at 4- under-par 209.
One of the players grouped with Stefani is 2012 champion Luke Donald (67). Donald was three strokes back of the leader entering the final round of this event last year before closing with a 6-under 66 and topping Furyk, Robert Garrigus and Sang-Moon Bae in a playoff.
"It was nice to go around this course not make a mistake, not drop a shot, and you know, I wanted to shoot 5- or 6-under, nearly got there, a couple missed putts and didn't birdie any par fives," Donald said. "Could have been a really low round today. But yeah, certainly moving in the right direction, as I said, I feel like my game has been close, and obviously starting to show with some results."
Streelman rolled through his front nine with two birdies and seven pars before making a strong push after the turn, starting when he chipped an errant drive at the 10th within eight feet and converted the birdie attempt.
He followed that a 6-foot birdie putt at the par-5 12th, and then rolled in a 15-foot birdie effort at the par-3 13th to move his way further up the leaderboard.
Streelman converted another birdie putt after hitting his tee shot within 13 feet of the pin at the par-3 17th to move into the top spot.
He closed his round with a par at the last to take the clubhouse lead.
Leonard, meanwhile, followed a birdie at the second with five straight pars before closing out his front nine with back-to-back birdies at the eighth and ninth, each of which came on putts of at least nine feet.
He then recovered from a greenside bunker at the 11th with a 6-foot birdie putt to grab a share of the lead, and briefly moved ahead at the 12th by converting a 9-foot birdie effort.
Leonard would not be able to hang on, however, as his tee shot at the par-3 15th found its way into a bunker before he 2-putted for bogey to fall back into a tie with Streelman.
Coetzee countered one bogey with four birdies during his round to move into contention for his first PGA Tour title.
NOTES: Streelman has three third-place finishes in his PGA Tour career, most recently at the 2010 Barclays. The last time Streelman held at least a share of a lead after 54 holes was at the 2010 Puerto Rico Open, which he finished in a tie for third ... Stefani is a rookie on the PGA Tour and hasn't finished inside the top 35 in his previous nine tour starts ... Leonard is in search of his 13th career PGA win and first since the 2008 FedEx St. Jude Classic ... Coetzee is in the field on a sponsor exemption ... The last 54-hole leader to go on and win this event was Furyk in 2010.