Hubbard's seven-under-par 65 on Saturday took him to 15 under par for the tournament, one shot clear of Canada's Mackenzie Hughes, who held the lead overnight and stayed in the hunt with a 68.
South Africa's Garrick Higgo (68) lies in a tie for third a further two shots back alongside Scott Stallings (68) and Sepp Straka (69).
Nick Hardy (68) and Keegan Bradley (64) are tied for sixth at 11 under, four shots back.
The day belonged to Hubbard, however, who had managed just one birdie in the first half of his round before reaching the 11th and notching up five in a row, before adding another at the 18th for good measure.
"I hit my irons great again. I feel like I actually did a better job with that today in terms of just leaving myself more makeable putts," said the American, who is chasing his maiden PGA Tour victory.
"I've been hitting it close all week, but a lot of them have been kind of in tough spots, downhill, down grain. That little stretch I went on, pretty much every putt was just dead straight up the hill, so that was really nice."
Second-placed Hughes mixed six birdies with two bogeys in his round, bouncing back from a bogey at the 17th with a closing birdie to stay just one shot back.
"That was huge," Hughes said. "I felt like I let one get away on 17, made a bad swing, kind of had a little distraction there on the tee, so that was unfortunate. But I knew coming up 18 that that was going to be a big hole for me for tomorrow, and making a 3 there was huge. It keeps me within striking distance of Mark, and he's been playing great, so it'll be a tough battle tomorrow."
Bradley's 64 was the low round of the day, and he credited a FaceTime chat with his coach after his second round for helping him rediscover some form.
"Today I hit more fairways," Bradley said. "I was just saying, if you hit the fairway on this course, every hole you can score on. But the rough is so brutal that you cannot if you don't. Today was a better day for hitting fairways for me."