Seeking his first victory on the U.S. circuit, American Stefani piled up eight birdies on the way to a four-under-par 66 on a warm day at the TPC Southwind, picking up four shots in his last five holes to post a 12-under total of 198.
Compatriot English, who had been two strokes in front of the chasing pack overnight in pursuit of his maiden PGA Tour title, rolled in a 14-footer to birdie the last for a 69 to secure outright second place.
"It's funny, I actually hit a good shot," Stefani, 31, told Golf Channel about his tee shot at the par-three 11th which ended up in water. "I just pulled the wrong club with the wrong wind. It happens.
"But it was a good day and I played good. It actually helped to have Harris along because he's a great young player and we have a lot of similarities in our lives and stuff. I had a great time with him and I'm looking forward to it tomorrow."
PGA Tour rookie Patrick Reed fired the day's lowest score, a six-birdie 64 lifting him into a tie for third at eight under with fellow Americans Nicholas Thompson (66) and Scott Stallings (67).
Four-times major champion Phil Mickelson also mounted a charge on what is traditionally known as 'Moving Day' at golf tournaments, a 65 putting him at seven under alongside rookie Eric Meierdierks (66).
"I've played better each round and I'm encouraged by that," Mickelson said after mixing an eagle at the par-five third with six birdies and three bogeys. "I could really get some glimpses of my game getting where I want it.
"Hopefully, I'll put together a really low round (on Sunday) and catch the leaders."
Several other big names were also in contention with triple major winner Padraig Harrington of Ireland (65) at six under, a stroke better than Englishman Ian Poulter and defending champion Dustin Johnson of the U.S. who returned matching 68s.
However the third round effectively came down to a head-to-head between Stefani and English as they vied for the lead.
English needed birdies at the first and third to remain two ahead of Stefani, who picked up shots at the second and third to get to 10 under.
The 23-year-old English then bogeyed the fifth and eighth to drop back into a tie for the lead before Stefani sank a six-foot birdie putt at the par-four ninth to move one stroke clear.
Stefani also birdied the 10th, rolling in a 12-footer there to briefly forge two ahead, before he ran up an ugly seven at the 11th that sent him tumbling back to eight under, two off the pace.
He found water off the tee, hit his third shot into the back left greenside bunker and took two more strokes to reach the green before two-putting from four feet for a seven.
"It was tough to watch," said English, who has recorded three top-10s in 16 starts on the 2013 PGA Tour, his best finish a tie for sixth at the Zurich Classic of New Orleans in April. "I don't care who you are.
"I am pulling for him, I'm pulling for anybody, but I'm also trying to beat him. It was tough to watch that but then he brought it back beautifully and played some solid golf out there."
Stefani steadily worked his way back into a tie for the lead, sinking an 11-footer for birdie at the 14th and then getting up and down from a greenside bunker to birdie the par-five 16th.
Further birdies followed at 17, where Stefani drained a 17-footer, and at the last, where he hit his approach to eight feet before coolly sinking the putt, as he ended the day on top.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Gene Cherry)