The Australian was far from his very best, but a two-under-par 69 at Conway Farms was enough to increase his lead after he started the day five shots clear.
He posted a 20-under 193 total with one round left in the third of the PGA Tour's four FedExCup playoff events.
Americans Scott Piercy (67) and Daniel Berger (70) shared second place at 14-under.
World number three Day, in posting the largest 54-hole lead on the PGA Tour this year, set himself up to claim the world number one ranking.
If he wins on Sunday, he will overtake current top dog Rory McIlroy, who shot 67 to be fourth at 13-under.
Day would also be the 19th player to earn top ranking, and the third Australian after Greg Norman and Adam Scott.
“I felt like I shot 80,” Day told reporters.
“So to be able to squeak out with a 69 and really feel like I got everything that I possibly could out of today's round, I think that was the best score I could have shot.
“It was a little clouded today, so I'm hoping that it's a lot more free tomorrow and I can just kind of think to myself and really kind of just push forward and not really worry about who's around me like I did today.”
If the 27-year-old Day can convert the large lead it will be his fifth win of the year after the Farmers Insurance Open, Canadian Open, PGA Championship (his first major title) and the Barclays, the latter three coming in his last five starts.
He would be the first international player with five wins on the American circuit since Vijay Singh, of Fiji, won nine times in 2004.
“I told everyone when I first came out that I wanted to become number one and everyone kind of laughed, and that's okay. That's kind of the dream that I've always had and now I've got an opportunity,” Day said.
“It's a lifelong dream. There's so many good things and good perks that come with being number one but it won't happen if I don't win tomorrow so I have to focus on the stuff that I've done to get to this point, and I think if I can do that, then I'll be able to pull off a win tomorrow.
(Editing by Andrew Both)
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