17 and 18, missed a handful of putts and finished bogey-double bogey to fall back to 14 under instead of 17 under which is where he was after the 16th.
Kang is vying for a win that would earn him an invitation to the Masters, the first major of the year that tees off next Thursday at Augusta National.
Overtaking Kang will be a challenge given his 36-hole lead, but Fowler is one clear of Russell Henley and two clear of the rest of the field so he'll have some breathing room to try and get his work done in Round 4.
"It's all about putting", said Kang, who has hit 15 of the course's 18 greens both days and needed just 25 putts Friday after only 27 on Thursday.
Kang heard the cheering and clapping from the preceding group following the popular Fowler, who delighted his overflowing gallery by picking up eight birdies in the first 14 holes, including a monster 50-footer putt at the seventh hole.
This was the third win on the PGA Tour for Henley. "I tried to really grind it out today and I did pretty good".
Henley had trailed Kang by four strokes going into the final round.
"I heard a lot of noise in front of us so I was like, 'Oh, I know something big is going on up there, '" Kang said.
"I'm starting to believe in myself and think 'why can't I win more?'".
Thompson seized the lead after 36 holes when she started off with back-to-back birdies and completed her second-round 67.
"It's not in my head", Kang said.
Argentine veteran Angel Cabrera was never in contention, but he delivered the spectacle of the day with his hole in one on the 226-yard ninth hole, his last of the day. She continued her strong play in the afternoon.
But at the other end of the leaderboard, former Masters winners Jordan Spieth and Adam Scott, 2016 runner-up Lee Westwood and Open champion Henrik Stenson all missed the halfway cut.
"I like playing my way into majors and they've been able to do a great job here making it as similar to possible of what we may see next week", Fowler told reporters.