But it was a disappointing day for Northern Ireland's Rory McIlroy after a two-over-par 73 saw the US Open champion fall out of contention.
Fowler began the day in a five-way tie for the lead which included McIlroy, but surged clear of the field with a fine effort that contained eight birdies and no dropped shots.
The 22-year-old American climbed to 13 under par, comfortably ahead of nearest challenger Yang who carded a 67.
"I had a good round and I can't complain with a 63," Fowler told OneAsia's official website.
"Going into the round I wanted to drive the ball well and make some putts, and I was able to do that and that puts me in a good position. My goals were to drive well and putt well, but my overall game was also good.
"I think I can win. I feel good about my game and I'm in a great position, which is right where I wanted to be coming into the week."
McIlroy, meanwhile, began his third round in encouraging fashion with birdies at the sixth and eighth.
But he then dropped six shots in eight holes - including one at the 12th where he thought he had played the wrong ball - before birdies at the 17th and 18th saw him eventually finish on three under for the tournament, 10 shots off the lead.
"I had a good finish, but it was not my best day," McIlroy said.
"I played quite nicely over the first few holes, but the pin positions were very tricky. I was two under through eight holes and I felt pretty good, but I missed a little putt on nine which threw me a little.
"I played 10 and 11 pretty well, but I hit a tee shot on 12 which I have not hit that wide all week.
"And after I hit my first ball out of bounds, I then hit my second in the rough and as I was taking a practice swing I hit another ball which I didn't see and at first the rules official said that I had played a wrong ball.
"I had no intention of hitting it, but I got it up and down with the other ball and thought I had made seven, but the rules official then said it was okay and I actually made five.
"That got into my head a little and I lost it a bit on the back nine and I got on a bit of a bad run, but I then played the final two holes a lot better after two good drives."
Yang posted six birdies and two bogeys in his 67 as the Korean reached nine under par for his week.
"Rickie and I had a good battle at the top of the leaderboard and I am satisfied with the round," Yang said.
"I made bogeys on the par fours after I hit bad tee shots, but if I can drive well in the final round, I have a chance to get a low score."