Wagner, who shared the lead after a brilliant first-round 62 before ending on Friday in joint second place, recorded seven birdies and dropped just the one shot as he moved to 14 under for the tournament.
That left the American with daylight between himself and nearest challenger Jimmy Walker, who also shot a 64 after picking up five of his six birdies on the back nine.
In third place on 10 under par is Sweden's Jonas Blixt - the only European in the top 20 - after he carded his second successive round of 67. Blixt recovered from a double bogey on 13 with birdies on 15 and 17 to earn a spot in the top three.
Behind him are a group of three players on nine under par, Australian duo Steven Bowditch (69) and Matt Jones (66) as well as American Jordan Spieth (67).
However, on another day where there were plenty of low scores at Old White TPC, one player who struggled badly was overnight leader Matt Every.
Every's 62 yesterday gave him a one-shot lead heading into the third round but he slumped down to joint 27th on five under following a real mixed bag of a day that saw him finish with a four-over-par 74.
Every could hardly have had a worse start, dropping shots on the first, second, sixth and seventh holes, before seemingly starting a recovery with back-to-back birdies following the turn.
However, he then recorded successive double-bogey sixes on the 13th and 14th to plummet back down the leaderboard. The American at least managed to regain some form over the closing holes though, picking up birdies on the 15th and 17th.
English duo Brian Davis and Greg Owen are also on five under par after rounds of 70 and 72 respectively.
Wagner vowed to attack on the final day.
He told www.pgatour.com: "This is the kind of golf course that if you play tentative at all you're going to miss fairways, and when you miss fairways out here you get some awkward angles on some of these tough Tour pins especially on Sunday.
"So I think my main key for tomorrow [Monday] is going to be aggressive off the tee and hit as many fairways as I can, which will set up a lot of birdie opportunities."